Class 12 Physics (Part 2) Chapter 14 Reflection of Light : Spherical Mirrors

This quiz on Class 12 Physics (Part 2), Chapter 14 – Reflection of Light: Spherical Mirrors is designed to assess students’ understanding of the fundamental concepts related to the behavior of light when it reflects from curved surfaces. It covers key topics such as the laws of reflection, types of spherical mirrors, mirror formula, focal length, radius of curvature, and the formation and characteristics of images by concave and convex mirrors. The quiz also includes conceptual and numerical questions on ray diagrams, sign conventions, and real-life applications of spherical mirrors in devices like headlights, telescopes, and shaving mirrors. Through this assessment, students will reinforce their conceptual clarity, analytical thinking, and problem-solving skills essential for mastering the optics unit in Class 12 Physics.

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Category: Sign Conventions (New Cartesian)

1. What is the sign of the focal length for a convex mirror according to the New Cartesian Sign Convention?

a) Negative

b) Positive

c) Zero

d) Depends on the object distance

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Category: Uses of Spherical Mirrors

2. An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. At what distance from the mirror will the real image be formed?

a) 10 cm behind the mirror

b) 15 cm in front of the mirror

c) 20 cm behind the mirror

d) 25 cm in front of the mirror

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Category: Concave Mirror:

3. What is the relationship between focal length ($f$), object distance ($u$), and image distance ($v$) for a concave mirror?

a) $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

b) $\frac{1}{v} \times \frac{1}{u} = \frac{1}{f}$

c) $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

d) $v + u = f$

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Category: Velocity of Image

4. (A) For a concave mirror, if an object moves towards the mirror with velocity $v_o$, the velocity of the image is always directed away from the mirror with magnitude greater than $v_o$ when magnification $\|m\| > 1$.
(R) The velocity of the image in a spherical mirror is given by $v_i = -m^2 v_o$, where $m$ is the magnification and $v_o$ is the velocity of the object.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Magnification

5. A small rod of length 2 cm is placed along the principal axis of a concave mirror of focal length 10 cm. One end of the rod is at a distance of 25 cm from the mirror. What is the length of the image of the rod?

a) $\frac{50}{3}$ cm

b) $\frac{40}{51}$ cm

c) $\frac{270}{17}$ cm

d) $\frac{17}{270}$ cm

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Category: Convex Mirror (Reflecting surface is outward)

6. A convex mirror forms an image that is one-fourth the size of the object. What is the magnification?

a) -1

b) -0.25

c) 0.25

d) 0.5

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Category: Concave Mirror:

7. An object is placed between the focus and the center of curvature of a concave mirror. Which statement about the image is correct?

a) The image is virtual, erect, and diminished

b) The image is real, inverted, and diminished

c) The image is real, inverted, and magnified

d) The image is virtual, erect, and magnified

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Category: Principal Focus (F)

8. Which of the following statements about the focal plane of a spherical mirror is correct?

a) It is parallel to the principal axis.

b) It passes through the centre of curvature.

c) It is perpendicular to the principal axis and passes through $F$.

d) It is tangent to the mirror surface.

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Category: Definition of Reflection

9. A ray of light is incident on a plane mirror at an angle of 30 degrees with the normal. What will be the angle between the incident ray and the reflected ray?

a) 30 degrees

b) 45 degrees

c) 60 degrees

d) 90 degrees

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Category: Between C & F → Beyond C, real, inverted, enlarged.

10. If an object is placed at 25 cm from a concave mirror with a focal length of 20 cm (between \$C\$ and \$F\$), what will be the magnification of the image?

a) 0.5

b) 2

c) -2

d) -4

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Category: For real image: m is negative.

11. Which of the following statements is true regarding the magnification ($m$) of an image formed by a spherical mirror?

a) A real image always has a positive magnification.

b) A virtual image always has a negative magnification.

c) The magnification for a real image is negative, and for a virtual image, it is positive.

d) The magnification for both real and virtual images is always positive.

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Category: Convex Mirror

12. What is the focal length of a convex mirror with radius of curvature 40 cm?

a) 10 cm

b) 20 cm

c) 30 cm

d) 40 cm

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Category: Concave Mirror:

13. A concave mirror has a radius of curvature of 24 cm. If an object is placed 18 cm from the mirror, what is the nature and position of the image formed?

a) Virtual, 36 cm behind the mirror

b) Real, 36 cm in front of the mirror

c) Virtual, 24 cm behind the mirror

d) Real, 24 cm in front of the mirror

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Category: Real image: negative magnification.

14. An object is placed $24 \, \text{cm}$ in front of a concave mirror with a focal length of $6 \, \text{cm}$. If the image formed is real, what is the magnification?

a) $-\frac{1}{2}$

b) $-\frac{1}{3}$

c) $-2$

d) $-3$

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Category: Concave: f, R negative; Convex: f, R positive.

15. A concave mirror with radius of curvature $-50$ cm is illuminated by both paraxial and non-paraxial rays (angle of incidence 45 degrees). Compare the focal lengths for these two cases.

a) Both are equal to $-25$ cm

b) Non-paraxial focal length is $-35.36$ cm, more negative than paraxial

c) Non-paraxial focal length is $-17.68$ cm, less negative than paraxial

d) Paraxial focal length is $-50$ cm

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Category: Street lamps for wide area illumination

16. Why is a convex mirror preferred as a driver's mirror in vehicles?

a) It magnifies the image of objects behind

b) It provides a wider field of view

c) It forms real images of distant objects

d) It reverses the image left-to-right

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Category: Principal Axis – Line joining P and C.

17. What is the principal axis of a spherical mirror?

a) A line perpendicular to the mirror surface at any point

b) The straight line joining the pole (P) and the center of curvature (C)

c) The line passing through the focus (F) and parallel to the mirror

d) The diameter of the mirror along its edge

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Category: Rear-view mirrors in vehicles

18. A convex rear-view mirror in a vehicle has a radius of curvature of 1.2 m. What is its focal length?

a) 0.3 m

b) 0.6 m

c) 1.2 m

d) 2.4 m

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Category: Focal Length (f) – Distance PF; f = R/2.

19. If the focal length ($f$) of a spherical mirror is \$10 \text{ cm}\$, what is its radius of curvature ($R$)?

a) \$5 \text{ cm}\$

b) \$10 \text{ cm}\$

c) \$15 \text{ cm}\$

d) \$20 \text{ cm}\$

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Category: Concave Mirror:

20. Where is the image formed when an object is placed at the center of curvature ($C$) of a concave mirror?

a) At focus ($F$)

b) Between $F$ and $P$

c) At $C$

d) Beyond $C$

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Category: Identification of Mirrors

21. A concave mirror forms an image that is real, inverted and three times the size of the object. If the object distance is 40 cm, what is the radius of curvature of the mirror?

a) 30 cm

b) 45 cm

c) 60 cm

d) 90 cm

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Category: Concave: f, R negative; Convex: f, R positive.

22. Which of the following correctly describes the sign convention for a convex mirror?

a) Both $f$ and $R$ are negative

b) $f$ is positive, $R$ is negative

c) $f$ is negative, $R$ is positive

d) Both $f$ and $R$ are positive

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Category: Part of a hollow sphere with a polished and reflecting surface.

23. If the radius of curvature of a convex mirror is 40 cm, what is its focal length?

a) 10 cm

b) 20 cm

c) 40 cm

d) 80 cm

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Category: Concave Mirror:

24. An object is placed 30 cm in front of a concave mirror with a radius of curvature of 20 cm. What is the nature and position of the image formed?

a) Real, inverted, and diminished, at 15 cm from the mirror

b) Virtual, erect, and enlarged, at 20 cm from the mirror

c) Real, inverted, and enlarged, at 30 cm from the mirror

d) Virtual, erect, and diminished, at 10 cm from the mirror

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Category: Relation Between Focal Length and Radius of Curvature

25. For a spherical mirror, what is the relationship between focal length (\$f\$) and radius of curvature (\$R\$) under paraxial approximation?

a) \$f = R\$

b) \$f = 2R\$

c) \$f = \frac{R}{2}\$

d) \$f = \frac{1}{R}\$

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Category: Types of reflection: Regular and Diffuse

26. In an experiment, a single ray of light is incident at 30° on both a perfect mirror and a white paper sheet. How do the angles of reflection compare in both cases?

a) Both show a single reflected ray at 30°

b) The mirror reflects at 30°, but the paper reflects at multiple angles

c) The mirror reflects at 60°, but the paper reflects at 30°

d) Both surfaces reflect light at multiple angles

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Category: Convex Mirror (Reflecting surface is outward)

27. Where is the image formed when an object is placed at infinity in front of a convex mirror?

a) At the center of curvature

b) At the focus

c) Between the pole and the focus

d) Behind the mirror

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Category: Magnification

28. A spherical mirror produces an image that is virtual, erect, and twice the size of the object. The mirror must be:

a) Plane mirror

b) Convex mirror

c) Concave mirror

d) Either convex or concave mirror

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Category: Beyond C → Between C & F, real, inverted, diminished.

29. An object is placed beyond the center of curvature (C) of a concave mirror. Where is the image formed and what is its nature?

a) At C, real and inverted

b) Between C and F, real, inverted, and diminished

c) Beyond C, virtual and erect

d) At F, highly diminished and virtual

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Category: Convex Mirror

30. An object is placed 60 cm in front of a convex mirror with a focal length of 30 cm. What is the magnification of the image formed?

a) $\dfrac{1}{2}$

b) $\dfrac{1}{3}$

c) $\dfrac{1}{4}$

d) $\dfrac{2}{3}$

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Category: Between C & F → Beyond C, real, inverted, enlarged.

31. A concave mirror forms a real image at 45 cm when the object is placed at 90 cm. What is the focal length of the mirror?

a) 15 cm

b) 20 cm

c) 30 cm

d) 45 cm

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Category: Convex Mirror

32. A convex mirror forms an image that is one-third the size of the object. If the image is located 15 cm behind the mirror, what is the object distance?

a) 45 cm

b) 30 cm

c) 60 cm

d) 90 cm

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Category: Between C & F → Beyond C, real, inverted, enlarged.

33. (A) When an object is placed between the center of curvature (C) and the focal point (F) of a concave mirror, the image formed is real, inverted, and enlarged.
(R) The mirror equation $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ confirms that for an object between C and F, the image distance $v$ is negative, indicating a real image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

34. In a concave mirror, where is the centre of curvature located with respect to the pole of the mirror?

a) On the right side of the pole (positive X-axis)

b) On the left side of the pole (negative X-axis)

c) At the pole itself

d) At infinity

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Category: Image Formation by Spherical Mirrors

35. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 15 cm. What is the nature and position of the image formed?

a) Real, inverted, and 30 cm from the mirror

b) Virtual, erect, and 30 cm from the mirror

c) Real, inverted, and 15 cm from the mirror

d) Virtual, erect, and 15 cm from the mirror

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Category: Ray diagrams for various object positions.

36. (A) For an object placed between the center of curvature (C) and the focus (F) of a concave mirror, the image formed is real, inverted, and magnified.
(R) In this case, the rays converge beyond the center of curvature after reflection, resulting in an enlarged image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Definition of Reflection

37. An object is placed at a distance of $20$ cm from a concave mirror of focal length $10$ cm. What is the image distance?

a) $-5$ cm

b) $-10$ cm

c) $-15$ cm

d) $-20$ cm

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Category: Rules for Image Formation

38. In a concave mirror, if the distance of an object from the focus is 10 cm and the distance of its real image from the focus is 40 cm, what is the focal length of the mirror?

a) 10 cm

b) 15 cm

c) 20 cm

d) 25 cm

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Category: Derived for both Concave and Convex mirrors

39. An object is placed at a distance of 30 cm from a concave mirror of focal length 15 cm. What is the image distance?

a) -15 cm

b) -30 cm

c) 30 cm

d) 15 cm

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Category: Concave Mirror:

40. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 10 cm. What is the nature and position of the image formed?

a) Real, inverted, at 15 cm from the mirror

b) Virtual, erect, at 15 cm from the mirror

c) Real, inverted, at 30 cm from the mirror

d) Virtual, erect, at 30 cm from the mirror

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Category: Introduction to Reflection

41. An object is placed at a distance of 10 cm from a convex mirror with a radius of curvature of 20 cm. What is the nature of the image produced?

a) Real and inverted

b) Virtual and erect

c) Real and enlarged

d) Virtual and diminished

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Category: Sign Conventions (New Cartesian)

42. If an image formed by a mirror is virtual and erect, what is the sign of its magnification?

a) Negative

b) Positive

c) Zero

d) Cannot be determined without additional information

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Category: Spherical Mirrors

43. For a spherical mirror, if the object distance ($u$) and image distance ($v$) are given, what is the correct mirror formula?

a) $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

b) $\frac{1}{v} + \frac{1}{u} = 2f$

c) $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

d) $v + u = f$

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Category: Ray obeys law of reflection at surface.

44. (A) A ray of light incident on a spherical mirror at an angle of $30^\circ$ to the normal will reflect at $30^\circ$ on the opposite side of the normal.
(R) According to the law of reflection, the angle of incidence is always equal to the angle of reflection.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Rules for Image Formation

45. A ray parallel to the principal axis is incident on a concave mirror. After reflection, where does it pass through?

a) Through the center of curvature (C)

b) Through the pole of the mirror

c) Appears to diverge from the focus

d) Through the focus (F)

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Category: Rules for Image Formation

46. What type of image is always formed by a convex mirror regardless of the object's position?

a) Real and inverted

b) Virtual and inverted

c) Real, erect, and magnified

d) Virtual, erect, and diminished

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Category: few Definitions Regarding Spherical Mirrors

47. (A) For a concave mirror, the pole is always at the midpoint between the centre of curvature and the focal point.
(R) The radius of curvature for a spherical mirror is twice its focal length.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Concave: f, R negative; Convex: f, R positive.

48. A concave mirror has a radius of curvature ($R$) of $-20$ cm. What is its focal length ($f$)?

a) 5 cm

b) $-5$ cm

c) 10 cm

d) $-10$ cm

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Category: Image Formation by Spherical Mirrors

49. An object is placed between the focus and center of curvature of a concave mirror. Which of the following correctly describes the nature of the image?

a) Virtual and erect

b) Real, inverted, and diminished

c) Real, inverted, and magnified

d) Virtual, inverted, and magnified

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Category: Ray through focus → becomes parallel to axis.

50. A ray of light is directed towards the focus of a convex mirror before reflection. What will be its behavior after reflection?

a) Converge at the center of curvature

b) Diverge away from the principal axis

c) Become parallel to the principal axis

d) Reflect back to the focus

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Category: Relation Between Focal Length and Radius of Curvature

51. A convex mirror has a focal length of 12 cm. What is its radius of curvature?

a) 6 cm

b) 36 cm

c) 24 cm

d) 48 cm

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Category: Derived for both Concave and Convex mirrors

52. For a concave mirror, if the object distance is 20 cm and the focal length is 10 cm, what is the image distance?

a) 5 cm

b) 10 cm

c) 20 cm

d) -20 cm

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Category: Laws of reflection

53. What happens to the path of a light ray when it strikes a smooth, polished surface like a mirror?

a) It gets absorbed completely by the surface

b) It scatters randomly in all directions

c) It bends away from the normal

d) It bounces back predictably according to the laws of reflection

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Category: Shaving mirror

54. A concave shaving mirror has a focal length of 0.4 m. If the magnification is 5, where should the face be placed relative to the mirror?

a) At 0.4 m from the mirror.

b) At 0.24 m from the mirror.

c) Beyond the center of curvature.

d) At infinity.

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Category: Velocity of Image

55. (A) For a convex mirror, if the object moves towards the mirror, the image moves away from the mirror.
(R) The velocity of the image in a convex mirror is given by $v_i = -m^2 v_o$, where $m$ is the magnification and $v_o$ is the velocity of the object.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Introduction to Reflection

56. An object is placed at a distance of 20 cm from a concave mirror of focal length 15 cm. What is the nature and position of the image formed?

a) Real, inverted, and magnified, at 60 cm from the mirror

b) Virtual, erect, and diminished, at 30 cm from the mirror

c) Real, erect, and same size, at 20 cm from the mirror

d) Virtual, inverted, and magnified, at 60 cm from the mirror

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Category: Between C & F → Beyond C, real, inverted, enlarged.

57. An object is placed 25 cm in front of a concave mirror with a focal length of 15 cm. Where will the image be formed and what will be its nature?

a) Image formed at 37.5 cm, virtual and erect

b) Image formed at 37.5 cm, real and inverted

c) Image formed at 60 cm, real and inverted

d) Image formed at 60 cm, virtual and erect

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Category: Rules for Image Formation

58. If an object is placed at a distance of 20 cm from a concave mirror with a focal length of 10 cm, what is the image distance using the mirror formula \$ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \$?

a) 10 cm

b) -20 cm

c) 20 cm

d) -10 cm

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Category: Radius of Curvature (R) – Distance PC.

59. For a concave mirror with a small aperture, if the radius of curvature is 30 cm, what is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

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Category: Types of reflection: Regular and Diffuse

60. What type of reflection occurs when light reflects off a smooth surface like a mirror?

a) Diffuse reflection

b) Scattered reflection

c) Irregular reflection

d) Regular reflection

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Category: Searchlights, headlights, solar cookers

61. Why are concave mirrors used in vehicle headlights?

a) To provide uniform illumination in all directions

b) To reduce glare for oncoming vehicles

c) To reflect light back towards the driver

d) To convert the diverging light from the bulb into a strong parallel beam

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Category: Laws of reflection

62. A concave mirror with a focal length of 20 cm forms an image at a distance of 30 cm from the mirror. What is the object distance if the image is real and inverted?

a) 40 cm

b) 50 cm

c) 60 cm

d) 70 cm

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Category: Between F & P → Behind mirror, virtual, erect, magnified.

63. When an object is placed between the focus (F) and the pole (P) of a concave mirror, what is the nature of the image formed?

a) Real and inverted

b) Virtual and inverted

c) Real and erect

d) Virtual and erect

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Category: Virtual erect image same size → Plane

64. (A) A mirror forms a virtual, erect, and same-sized image of an object placed in front of it.
(R) The mirror must be a plane mirror as only plane mirrors produce images that are virtual, erect, and of the same size as the object.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: At finite distance → Between P & F, virtual, erect, diminished.

65. An object is placed in front of a convex mirror. What can be said about the magnification ($m$) of the image formed?

a) Always negative and greater than 1

b) Always positive and less than 1

c) Always positive and greater than 1

d) Always negative and less than 1

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Category: Shaving mirror

66. Under what condition does a concave mirror form a virtual image?

a) When the object is placed at infinity

b) When the object is placed at the center of curvature

c) When the object is placed beyond the center of curvature

d) When the object is placed between the pole and the focus

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Category: Pole = origin, principal axis = X-axis.

67. (A) In the coordinate system used for spherical mirrors, the pole is taken as the origin (0, 0).
(R) The principal axis is designated as the X-axis because it passes through the pole and the center of curvature of the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Real image: negative magnification.

68. A concave mirror produces a real image at a distance of $30 \, \text{cm}$ when the object is placed at $15 \, \text{cm}$ from the mirror. What is the focal length of the mirror?

a) $-5 \, \text{cm}$

b) $-10 \, \text{cm}$

c) $-15 \, \text{cm}$

d) $-20 \, \text{cm}$

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Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

69. According to the New Cartesian Sign Convention, what is the sign of the radius of curvature $R$ for a concave mirror?

a) Positive

b) Negative

c) Zero

d) Undefined

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Category: Street lamps for wide area illumination

70. What is the main purpose of using a convex mirror in street lamps?

a) To focus light on a small specific spot

b) To concentrate all light rays parallelly

c) To diverge light and illuminate a large area

d) To reflect light back to the source

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Category: Introduction to Reflection

71. Which type of spherical mirror has its reflecting surface curved inwards?

a) Plane mirror

b) Convex mirror

c) Concave mirror

d) Biconvex mirror

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Category: Focal Length (f) – Distance PF; f = R/2.

72. What is the focal length ($f$) of a concave mirror if its radius of curvature ($R$) is \$-20 \text{ cm}\$?

a) \$5 \text{ cm}\$

b) \$-10 \text{ cm}\$

c) \$10 \text{ cm}\$

d) \$-5 \text{ cm}\$

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Category: Part of a hollow sphere with a polished and reflecting surface.

73. What is the pole of a spherical mirror?

a) The centre of the sphere from which the mirror is cut

b) The midpoint between the focus and centre of curvature

c) The central point of the reflecting surface of the mirror

d) The point where light rays converge after reflection

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Category: Reflecting telescopes

74. Which of the following is a key advantage of reflecting telescopes over refracting telescopes?

a) They are smaller in size compared to refracting telescopes.

b) They do not suffer from chromatic aberration.

c) They require less maintenance due to simpler design.

d) They can be used during daytime only.

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Category: Virtual image: positive magnification.

75. (A) A convex mirror always forms a virtual image with positive magnification.
(R) For a convex mirror, the image distance ($v$) is always positive and the magnification ($m$) is given by $m = -\frac{v}{u}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Mirror Formula

76. For a concave mirror, if the object distance from the focus is 8 cm and the image distance from the focus is 18 cm, what is the focal length of the mirror?

a) 10 cm

b) 12 cm

c) 14 cm

d) 16 cm

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Category: Relation Between Focal Length and Radius of Curvature

77. A concave mirror with radius of curvature R forms a real image at distance f from its pole when an object is placed at infinity. If this mirror is now submerged in water ($\mu$ = 4/3), what will be the new focal length?

a) $\frac{R}{3}$

b) $\frac{R}{2}$

c) $\frac{2R}{3}$

d) $\frac{3R}{4}$

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Category: Velocity of Image

78. A convex mirror has a focal length of 10 cm. An object moves perpendicular to the principal axis with a velocity of 8 cm/s. If the magnification at that instant is $+0.5$, what is the velocity of the image?

a) 2 cm/s opposite to the object's motion

b) 4 cm/s along the object's motion

c) 16 cm/s opposite to the object's motion

d) 8 cm/s along the object's motion

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Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

79. For a small-aperture spherical mirror, what is the relationship between focal length $f$ and radius of curvature $R$?

a) $f = 2R$

b) $f = \frac{R}{4}$

c) $f = \frac{R}{2}$

d) $f = R^2$

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Category: For real image: m is negative.

80. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 10 cm. What is the magnification of the image formed?

a) $-0.5$

b) $+0.5$

c) $-1.5$

d) $+1.5$

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Category: Pole (P) – Geometric center of the mirror.

81. An object placed in front of a concave mirror produces an image at twice the distance of the object from the pole. If the image is real and inverted, what is the ratio of the height of the image to the height of the object?

a) 1:1

b) 1:2

c) 2:1

d) 3:1

82 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

82. What is the focal plane of a spherical mirror?

a) A plane parallel to the principal axis passing through the center of curvature.

b) A plane perpendicular to the principal axis passing through the pole of the mirror.

c) A plane perpendicular to the principal axis passing through the principal focus.

d) A plane inclined at 45 degrees to the principal axis passing through the focus.

83 / 560

Category: Virtual image: positive magnification.

83. If an object is placed 10 cm in front of a concave mirror with a focal length of 15 cm, what is the magnification?

a) 1.5

b) -1.5

c) 3

d) -3

84 / 560

Category: Sign Conventions (New Cartesian)

84. An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. The image formed is real and inverted. What will be the magnification and nature of the image?

a) Magnification = $-2$, virtual and erect

b) Magnification = $-0.5$, real and inverted

c) Magnification = $+0.5$, virtual and erect

d) Magnification = $+2$, real and inverted

85 / 560

Category: Radius of Curvature (R) – Distance PC.

85. A convex mirror has a radius of curvature of 60 cm. What is its focal length?

a) 15 cm

b) 30 cm

c) -30 cm

d) -15 cm

86 / 560

Category: Types of reflection: Regular and Diffuse

86. Which type of reflection causes light to scatter in many different directions?

a) Regular reflection

b) Specular reflection

c) Diffuse reflection

d) Parallel reflection

87 / 560

Category: Real image: negative magnification.

87. A concave mirror has a focal length of 15 cm. If an object is placed at a distance of 30 cm from the mirror, what is the magnification of the image formed?

a) Magnification is $-1$

b) Magnification is $-2$

c) Magnification is $1$

d) Magnification is $0.5$

88 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

88. (A) When an object is placed between the focus (\$F\$) and the pole (\$P\$) of a concave mirror, the image formed is virtual and erect.
(R) The image formed behind the mirror is magnified because it lies beyond the center of curvature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

89 / 560

Category: Ray through center → retraces path.

89. What occurs when a light ray is directed towards the center of curvature $C$ of a convex mirror?

a) The ray converges towards the focus.

b) The ray reflects perpendicular to the principal axis.

c) The ray retraces its path.

d) The ray disappears inside the mirror.

90 / 560

Category: Principal Focus (F)

90. Two mirrors, one concave ($R = 40 \text{ cm}$) and one convex ($R = 60 \text{ cm}$), are placed side by side. A parallel beam of light falls on both mirrors. How far apart are their respective principal foci?

a) 10 cm

b) 20 cm

c) 50 cm

d) 70 cm

91 / 560

Category: Radius of Curvature (R) – Distance PC.

91. What is the focal length of a concave mirror if its radius of curvature is 30 cm?

a) $-10 \, \text{cm}$

b) $-15 \, \text{cm}$

c) $-20 \, \text{cm}$

d) $15 \, \text{cm}$

92 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

92. For a concave mirror with radius of curvature $R = 20$ cm, what is its focal length $f$?

a) 5 cm

b) 10 cm

c) 20 cm

d) 40 cm

93 / 560

Category: Real image: negative magnification.

93. Which of the following is true for a real image formed by a concave mirror?

a) Erect and has positive magnification

b) Inverted and has positive magnification

c) Erect and has negative magnification

d) Inverted and has negative magnification

94 / 560

Category: Identification of Mirrors

94. (A) A convex mirror always forms a virtual, erect, and diminished image of an object placed in front of it.
(R) The focal length of a convex mirror is positive according to the Cartesian sign convention.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

95 / 560

Category: Convex Mirror

95. An object is placed 40 cm in front of a convex mirror with a focal length of 10 cm. Where will the image be formed?

a) 6 cm behind the mirror

b) 8 cm behind the mirror

c) 12 cm behind the mirror

d) 16 cm behind the mirror

96 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

96. A concave mirror has an aperture of 15 cm and a focal length of 10 cm. If the incident light beam covers the entire aperture, what is the angle subtended by the extreme marginal rays at the focal point?

a) $30.96^\circ$

b) $36.87^\circ$

c) $45.00^\circ$

d) $53.13^\circ$

97 / 560

Category: Rules to Trace the Image Formed by Spherical Mirrors

97. (A) For a concave mirror, if an object is placed at the focus, the image formed is real and highly magnified.
(R) According to the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$, when $u = f$, the image distance $v$ approaches infinity, indicating a highly magnified image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

98 / 560

Category: Searchlights, headlights, solar cookers

98. (A) Parabolic mirrors are used in searchlights instead of concave spherical mirrors.
(R) A parabolic mirror reflects all incident rays parallel when the source is placed at its focus, whereas a concave spherical mirror causes spherical aberration.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

99 / 560

Category: Pole = origin, principal axis = X-axis.

99. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 20 cm. The image formed is real, inverted, and magnified. What is the position of the image?

a) -15 cm

b) -60 cm

c) 45 cm

d) 12 cm

100 / 560

Category: Image Formation by Spherical Mirrors

100. An object is placed 20 cm in front of a convex mirror with a focal length of 10 cm. What is the magnification of the image formed?

a) 2

b) 1/2

c) 1/3

d) 1/4

101 / 560

Category: Spherical Mirrors

101. An object is placed 30 cm in front of a convex mirror with a focal length of 15 cm. What is the image distance?

a) -10 cm

b) -5 cm

c) 10 cm

d) 15 cm

102 / 560

Category: Reflecting telescopes

102. (A) A paraboloidal mirror is used in reflecting telescopes to avoid spherical aberration.
(R) A paraboloidal mirror brings a wide beam of parallel rays to a precise point-focus, enhancing image clarity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

103 / 560

Category: Ray through center → retraces path.

103. (A) A light ray directed towards the center of curvature of a convex mirror will return back on the same path after reflection.

(R) The angle of incidence ($i$) for such a ray is zero, so the angle of reflection ($r$) is also zero as per the laws of reflection.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

104 / 560

Category: Principal Focus (F)

104. A mirror forms a virtual and diminished image of an object placed in front of it. Where is the principal focus ($F$) of this mirror located?

a) In front of the mirror and real

b) Behind the mirror and virtual

c) At the centre of curvature

d) At infinity

105 / 560

Category: Street lamps for wide area illumination

105. (A) Convex mirrors are used as reflectors in street lamps because they diverge light over a wide area.
(R) The divergent beam from a convex mirror ensures broader coverage, making it suitable for illuminating large spaces like streets.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

106 / 560

Category: Identification of Mirrors

106. An object is placed at a distance of 30 cm from a concave mirror of focal length 20 cm. The magnification produced by the mirror is:

a) $+2$

b) $-2$

c) $+0.5$

d) $-0.5$

107 / 560

Category: Concave Mirror:

107. (A) An object placed at the center of curvature ($C$) of a concave mirror forms an image of the same size as the object.
(R) For an object placed at $C$ of a concave mirror, the image distance ($v$) equals the object distance ($u$).

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

108 / 560

Category: Street lamps for wide area illumination

108. (A) A convex mirror is used as a reflector in street lamps because it can diverge light over a wide area.
(R) The diverging nature of a convex mirror allows it to cover a larger field of view compared to a plane mirror of the same size.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

109 / 560

Category: Shaving mirror

109. (A) A concave mirror is used for shaving because it always forms a real and inverted image of the face.
(R) For shaving, the face must be placed between the focus and the center of curvature of the concave mirror to get an enlarged image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

110 / 560

Category: Rules for Image Formation

110. A convex mirror has a radius of curvature of 40 cm. If an object is placed 20 cm from the mirror, what will be the magnification of the image?

a) 0.25

b) 0.5

c) 1.0

d) 2.0

111 / 560

Category: Real image: negative magnification.

111. (A) A concave mirror forms a real image with magnification $-2$.
(R) The negative sign in magnification indicates that the image is inverted.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

112 / 560

Category: Concave Mirror:

112. (A) For a concave mirror, if the magnification produced is -2 and the object is placed at a distance of 15 cm from the mirror, the image formed is real and inverted.
(R) The magnification formula for a concave mirror is given by $m = -\frac{v}{u}$, where $v$ is negative for real images.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

113 / 560

Category: Ray obeys law of reflection at surface.

113. A convex mirror has a focal length of 15 cm. A ray of light parallel to the principal axis is incident on the mirror. After reflection, the ray appears to diverge from a point 7.5 cm behind the mirror. What is the radius of curvature of the mirror?

a) 7.5 cm

b) 15 cm

c) 30 cm

d) 60 cm

114 / 560

Category: Magnification

114. (A) For a concave mirror, if an object moves towards the mirror along the principal axis with velocity $V_{om}$, the image will move away from the mirror with velocity $V_{im} = -m^2 V_{om}$.
(R) The negative sign in $V_{im} = -m^2 V_{om}$ indicates that the direction of the image velocity is opposite to that of the object velocity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

115 / 560

Category: Types of reflection: Regular and Diffuse

115. Which of the following best describes regular reflection?

a) Light scatters in all directions after reflection

b) Reflected rays remain parallel and create a clear image

c) Light is absorbed completely by the surface

d) The reflected rays do not follow the law of reflection

116 / 560

Category: Magnification

116. A convex mirror has a focal length of 15 cm. If the magnification produced is $+0.5$, where is the object placed?

a) 7.5 cm from the mirror

b) 15 cm from the mirror

c) 30 cm from the mirror

d) 45 cm from the mirror

117 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

117. A spherical mirror with an aperture of 12 cm forms an image of a distant object. If the mirror's radius of curvature is 24 cm, which of the following statements about aberrations caused by marginal rays is correct?

a) Marginal rays cause chromatic aberration.

b) Marginal rays converge exactly at the paraxial focus.

c) Marginal rays cause spherical aberration, leading to a blurred image.

d) Marginal rays do not contribute to any aberration.

118 / 560

Category: Uses of Spherical Mirrors

118. Why is a concave mirror preferred over a plane mirror for shaving?

a) It produces a smaller and inverted image.

b) It produces an enlarged and inverted image.

c) It produces an enlarged and erect image.

d) It produces a smaller and erect image.

119 / 560

Category: Convex Mirror

119. A convex mirror has a radius of curvature of 30 cm. What is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

120 / 560

Category: Concave Mirror:

120. An object is placed 30 cm in front of a concave mirror with a focal length of 15 cm. The image formed is:

a) Real, inverted, and same size as the object

b) Virtual, erect, and magnified

c) Real, inverted, and diminished

d) No image is formed

121 / 560

Category: Ophthalmoscopes, ENT examinations

121. An ENT specialist uses a concave mirror to examine a patient's throat. The mirror is placed 10 cm away from the throat and forms an image at a distance of 15 cm from the mirror. If an ophthalmologist uses the same mirror to examine the retina, what could be the possible range for the focal length of the mirror?

a) 4 cm to 8 cm

b) 5 cm to 10 cm

c) 6 cm to 12 cm

d) Exactly 6 cm

122 / 560

Category: Relation Between Focal Length and Radius of Curvature

122. If the angle of incidence of a non-paraxial ray on a concave mirror is 30°, how does the focal length change compared to the paraxial case? Assume $R = 40$ cm.

a) Focal length decreases to 10 cm

b) Focal length remains the same

c) Focal length increases to approximately 23.09 cm

d) Focal length becomes zero

123 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

123. A convex mirror with a focal length of 10 cm forms an image of an object placed 30 cm from the mirror. What is the magnification of the image?

a) 0.50

b) 0.25

c) 0.33

d) 0.75

124 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

124. A concave mirror has a radius of curvature of 30 cm. If light rays make an angle of 45° with the principal axis, what is the effective focal length of the mirror for these non-paraxial rays?

a) 15.00 cm

b) 21.21 cm

c) 25.50 cm

d) 30.00 cm

125 / 560

Category: Ray through focus → becomes parallel to axis.

125. For a spherical mirror with a small aperture, what is the relationship between the radius of curvature $R$ and the focal length $f$?

a) $f = \frac{R}{4}$

b) $f = \frac{R}{3}$

c) $f = \frac{R}{2}$

d) $f = 2R$

126 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

126. An object is placed between the focus (F) and pole (P) of a concave mirror. What will be the nature of the image formed?

a) Real, inverted, and diminished

b) Virtual, inverted, and magnified

c) Virtual, erect, and diminished

d) Virtual, erect, and magnified

127 / 560

Category: Velocity of Image

127. An object moves perpendicular to principal axis at speed $8\text{ cm/s}$ towards a concave mirror ($f=12\text{ cm}$) while being at $u=18\text{ cm}$. What is the image speed component perpendicular to principal axis if the image is virtual?

a) 6.4 cm/s in same direction

b) 3.2 cm/s in same direction

c) 2.0 cm/s in opposite direction

d) 1.6 cm/s in opposite direction

128 / 560

Category: Reflecting telescopes

128. In a Newtonian reflecting telescope, what is the function of the secondary mirror?

a) To collect light from distant objects

b) To magnify the image before it reaches the eyepiece

c) To reflect light to the side of the telescope tube for viewing

d) To eliminate chromatic aberration

129 / 560

Category: Principal Axis – Line joining P and C.

129. A concave mirror has a radius of curvature $R = 40 \, \text{cm}$. An object is placed at a distance of $60 \, \text{cm}$ from the pole on the principal axis. What is the image distance from the pole?

a) 10 cm

b) 15 cm

c) 30 cm

d) 45 cm

130 / 560

Category: Street lamps for wide area illumination

130. A convex mirror and a concave mirror are placed such that their reflecting surfaces face each other and their principal axes coincide. The focal lengths of the convex and concave mirrors are 10 cm and 15 cm, respectively. If an object is placed 20 cm from the convex mirror, what is the final image position after reflection from both mirrors?

a) 40 cm

b) 50 cm

c) 60 cm

d) 70 cm

131 / 560

Category: Spherical Mirrors

131. A concave mirror forms a real image three times the size of the object when the object is placed 30 cm from the mirror. What is the radius of curvature of the mirror?

a) Magnification ($m$) = -3 (real image, inverted)

b) Object distance ($u$) = -30 cm (negative as per sign convention) \end{itemize} First, find the image distance ($v$) using magnification formula: $m = -\frac{v}{u}$ $-3 = -\frac{v}{-30}$ $-3 = \frac{v}{30}$ $v = -90 \, \text{cm}$ Now, use the mirror formula to find the focal length ($f$): $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ $\frac{1}{f} = \frac{1}{-90} + \frac{1}{-30}$ $\frac{1}{f} = -\frac{1}{90} - \frac{1}{30}$ $\frac{1}{f} = -\frac{1 + 3}{90} = -\frac{4}{90} = -\frac{2}{45}$ $f = -\frac{45}{2} = -22.5 \, \text{cm}$ Radius of curvature ($R$) is twice the focal length: $R = 2f = 2 \times (-22.5) = -45 \, \text{cm}$ The negative sign indicates the mirror is concave. Hence, the radius of curvature is 45 cm.

c) 30 cm

d) 40 cm

e) 45 cm

f) 60 cm

132 / 560

Category: Uses of Spherical Mirrors

132. Why is a concave mirror preferred over a plane mirror for shaving?

a) It provides a diminished real image

b) It produces an enlarged virtual image when the face is between the pole and focus

c) It reduces glare from surrounding light

d) It does not reflect any image

133 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

133. A concave mirror has a focal length of 20 cm. If an object is placed 40 cm from the mirror, what is the position and nature of the image?

a) At 20 cm, virtual and erect

b) At 40 cm, real, inverted, and same size

c) At infinity, real and highly diminished

d) Between C and F, real and diminished

134 / 560

Category: Numerical Problems

134. A concave mirror produces a real, four times magnified image of an object placed at 10 cm in front of it. Find the position of the image ($v$) and the radius of curvature ($R$).

a) $v = -40 \, \text{cm}, R = -16 \, \text{cm}$

b) $v = 40 \, \text{cm}, R = 16 \, \text{cm}$

c) $v = -20 \, \text{cm}, R = -10 \, \text{cm}$

d) $v = 20 \, \text{cm}, R = 10 \, \text{cm}$

135 / 560

Category: Laws of reflection

135. Which of the following statements correctly describes the behavior of a light ray when it reflects off a plane mirror?

a) The incident ray and reflected ray lie in different planes

b) The incident ray bends towards the normal after reflection

c) The incident ray and reflected ray make equal angles with the normal and lie in the same plane

d) The reflected ray disappears after hitting the mirror

136 / 560

Category: Pole = origin, principal axis = X-axis.

136. An image formed by a convex mirror is located 8 cm below the principal axis. What is the correct sign of the image height?

a) $h' = +8$ cm

b) $h' = -8$ cm

c) $h' = +4$ cm

d) $h' = -4$ cm

137 / 560

Category: Ray obeys law of reflection at surface.

137. What does the law of reflection state for a ray incident on a spherical mirror?

a) The angle of incidence is greater than the angle of reflection.

b) The angle of incidence is less than the angle of reflection.

c) The angle of incidence is equal to the angle of reflection.

d) The angle of incidence is twice the angle of reflection.

138 / 560

Category: Convex Mirror

138. A convex mirror forms an image with a magnification of 0.25. If the object distance is 60 cm, what is the focal length of the mirror?

a) 10 cm

b) 15 cm

c) 20 cm

d) 25 cm

139 / 560

Category: Identification of Mirrors

139. (A) A mirror producing a virtual, erect, and magnified image is concave.
(R) Concave mirrors always produce magnified images.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

140 / 560

Category: Velocity of Image

140. A moving object's distance from concave mirror ($f=15\text{ cm}$) changes from $u_1=45\text{ cm}$ to $u_2=30\text{ cm}$ in 2 seconds. What is the average speed of the image during this interval?

a) 1.25 cm/s

b) 3.75 cm/s

c) 5.50 cm/s

d) 7.25 cm/s

141 / 560

Category: Ray obeys law of reflection at surface.

141. For a concave mirror, if an incident ray passes through the center of curvature, what will be the path of the reflected ray?

a) It reflects parallel to the principal axis

b) It reflects perpendicular to the principal axis

c) It retraces its path back through the center of curvature

d) It diverges away from the principal axis

142 / 560

Category: Definition of Reflection

142. Which type of spherical mirror has its reflecting surface towards the center of the sphere of which the mirror is a part?

a) Plane mirror

b) Convex mirror

c) Concave mirror

d) Parabolic mirror

143 / 560

Category: Mirror Formula

143. If an object is placed at a distance of 20 cm from a convex mirror with a focal length of 10 cm, what is the magnification produced by the mirror?

a) $\frac{1}{3}$

b) $\frac{2}{3}$

c) $\frac{3}{2}$

d) $\frac{1}{2}$

144 / 560

Category: Identification of Mirrors

144. Why is a concave mirror preferred for shaving over a plane mirror?

a) It reflects less light

b) It forms a magnified and erect image

c) It has a wider field of view

d) It is cheaper to manufacture

145 / 560

Category: Ophthalmoscopes, ENT examinations

145. What is the purpose of using a concave mirror in an ophthalmoscope?

a) To magnify the image of the retina

b) To reflect light onto the retina for illumination

c) To reduce glare from external light sources

d) To focus X-rays onto the eye

146 / 560

Category: Coordinate Geometry Sign Convention for Measuring Distances and Lengths

146. (A) In the New Cartesian Convention, distances measured to the right of the pole along the principal axis are taken as positive.
(R) The pole of the mirror is taken as the origin in the coordinate system.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

147 / 560

Category: Ophthalmoscopes, ENT examinations

147. (A) Concave mirrors are used in ophthalmoscopes to examine the retina because they provide a magnified and clear image of the fundus.
(R) A concave mirror converges light rays to illuminate the retina effectively, allowing detailed examination through the central aperture.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

148 / 560

Category: Concave Mirror:

148. What type of image is formed by a concave mirror when the object is placed between the focus ($F$) and the pole ($P$)?

a) Real and inverted

b) Virtual and erect

c) Real and erect

d) Virtual and inverted

149 / 560

Category: Searchlights, headlights, solar cookers

149. (A) Concave mirrors are used in searchlights because they can produce a parallel beam of light.
(R) A concave mirror reflects light from its focus as a perfectly parallel beam when the mirror is paraboloidal.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

150 / 560

Category: Pole = origin, principal axis = X-axis.

150. A convex mirror forms an erect image of an object placed at 10 cm from it. If the magnification produced is 0.5, what is the radius of curvature of the mirror?

a) 40 cm

b) 20 cm

c) 5 cm

d) 10 cm

151 / 560

Category: Introduction to Reflection

151. When an object is placed between the pole and the focus of a concave mirror, what type of image is formed?

a) Real and diminished

b) Virtual and diminished

c) Real and enlarged

d) Virtual and enlarged

152 / 560

Category: Pole = origin, principal axis = X-axis.

152. What is the origin of the coordinate system when the pole (P) of a spherical mirror is taken as the reference point?

a) Centre of curvature

b) Focus

c) Pole

d) Aperture center

153 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

153. A concave mirror forms a real image that is half the size of the object. If the focal length is 12 cm, what is the object distance?

a) 24 cm

b) 36 cm

c) 48 cm

d) 60 cm

154 / 560

Category: few Definitions Regarding Spherical Mirrors

154. A ray of light is incident on a convex mirror parallel to its principal axis. After reflection, this ray appears to diverge from a point that is located:

a) At the center of curvature

b) Between the pole and focus

c) At the principal focus

d) Beyond the center of curvature

155 / 560

Category: Ray parallel to axis → passes through focus.

155. An object is placed at infinity in front of a convex mirror. Where will its image appear?

a) At the center of curvature

b) At the pole of the mirror

c) At the focus of the mirror

d) Between the focus and pole

156 / 560

Category: For real image: m is negative.

156. (A) For a concave mirror, if the magnification $m$ is negative, the image formed is real and inverted.
(R) The negative sign in magnification indicates that the image distance $v$ is negative for a real image, and the image is inverted.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

157 / 560

Category: Virtual image: positive magnification.

157. For a concave mirror, when is the magnification positive?

a) When the object is beyond the center of curvature

b) When the object is at the focus

c) When the object is between the pole and the focus

d) When the object is at infinity

158 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

158. What is the centre of curvature of a spherical mirror?

a) The point where light rays meet after reflection

b) The geometric center of the mirror surface

c) The center of the sphere of which the mirror is a part

d) The midpoint between the pole and focus of the mirror

159 / 560

Category: Convex Mirror

159. (A) A convex mirror always forms a virtual and diminished image regardless of the object's position.
(R) The focal length of a convex mirror is positive, and its images are formed by the apparent intersection of diverging rays.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

160 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

160. In the context of spherical mirrors, what does $MM'$ represent?

a) The principal axis of the mirror

b) The focal point of the mirror

c) The aperture (diameter) of the mirror

d) The radius of curvature of the mirror

161 / 560

Category: Virtual image: positive magnification.

161. What is the magnification produced by a convex mirror if the image size is 1 cm and the object size is 2 cm?

a) 0.5

b) -0.5

c) 2

d) -2

162 / 560

Category: Concave Mirror (Reflecting surface is inward)

162. What type of image is formed by a concave mirror when the object is placed between the focus $(F)$ and the center of curvature $(C)$?

a) Real, erect, enlarged

b) Virtual, erect, diminished

c) Real, inverted, magnified

d) Virtual, inverted, same size

163 / 560

Category: Paraxial Rays vs. Marginal Rays

163. Which of the following statements is true regarding the application of the mirror formula $1/f = 1/v + 1/u$?

a) It applies only to paraxial rays in small-aperture mirrors.

b) It applies to both paraxial and marginal rays equally.

c) It is invalid for all types of mirrors.

d) It can be used for any ray as long as the mirror is spherical.

164 / 560

Category: Ray parallel to axis → passes through focus.

164. A ray of light parallel to the principal axis is incident on a concave mirror with focal length 20 cm. After reflection, where does this ray pass through?

a) The center of curvature

b) The pole of the mirror

c) A point 40 cm from the pole

d) The focus of the mirror

165 / 560

Category: Rear-view mirrors in vehicles

165. A car's convex rear-view mirror has a focal length of 20 cm. If an approaching truck is located 80 cm behind the car, what is the magnification of the image formed by the mirror?

a) 0.1

b) 0.2

c) 0.3

d) 0.4

166 / 560

Category: Pole = origin, principal axis = X-axis.

166. An object is placed 10 cm to the left of the pole of a spherical mirror. According to the Cartesian sign convention, what is the correct representation of the object distance?

a) $u = +10$ cm

b) $u = -10$ cm

c) $u = +5$ cm

d) $u = -5$ cm

167 / 560

Category: Introduction to Reflection

167. A ray of light strikes a concave mirror parallel to its principal axis. After reflection, the ray will pass through:

a) Centre of curvature

b) Pole of the mirror

c) Focus of the mirror

d) None of the above

168 / 560

Category: Identification of Mirrors

168. What type of mirror is used in car rearview mirrors and why?

a) Concave mirror, as it magnifies images

b) Plane mirror, as it gives accurate-sized images

c) Convex mirror, as it provides a wider field of view

d) Parabolic mirror, as it reflects parallel beams accurately

169 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

169. Under what condition is the concept of a focal plane strictly valid for spherical mirrors?

a) For mirrors of any aperture size

b) Only for parabolic mirrors

c) Only for mirrors with large apertures

d) Only for mirrors with small apertures under paraxial approximation

170 / 560

Category: Rear-view mirrors in vehicles

170. (A) Rear-view mirrors in vehicles are convex mirrors because they provide a wider field of view.
(R) Convex mirrors produce diminished, virtual, and erect images.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

171 / 560

Category: Uses of Spherical Mirrors

171. What advantage does a convex mirror provide in vehicle side mirrors?

a) It gives a magnified image of distant objects

b) It has a narrower field of view than a plane mirror

c) It produces inverted images of vehicles behind

d) It provides a wider field of view with small, erect images

172 / 560

Category: Virtual image: positive magnification.

172. A concave mirror (f = -15 cm) produces a virtual image with magnification +3. Where should the object be placed?

a) 5 cm from mirror

b) 10 cm from mirror

c) 20 cm from mirror

d) 30 cm from mirror

173 / 560

Category: Uses of Spherical Mirrors

173. A concave mirror has a focal length of 20 cm. An object is placed 15 cm in front of the mirror. What is the nature and position of the image formed?

a) Virtual, erect, and located 30 cm behind the mirror

b) Real, inverted, and located 60 cm in front of the mirror

c) Virtual, erect, and located 60 cm behind the mirror

d) Real, inverted, and located 30 cm in front of the mirror

174 / 560

Category: Sign Conventions (New Cartesian)

174. A convex mirror forms a virtual image at a distance of 20 cm from its focus. If the object is placed 45 cm from the pole, what is the focal length of the mirror?

a) 30 cm

b) 22.36 cm

c) 40 cm

d) 50 cm

175 / 560

Category: Ray through center → retraces path.

175. Which statement is true for both concave and convex mirrors regarding rays aligned with the center of curvature?

a) Only concave mirrors exhibit this behavior.

b) The ray always diverges away from the principal axis.

c) The ray retraces its path in both types of mirrors.

d) The ray reflects at $90^\circ$ to the principal axis.

176 / 560

Category: Relation Between Focal Length and Radius of Curvature

176. For a concave mirror, if the radius of curvature is 40 cm, what is its focal length?

a) 10 cm

b) -10 cm

c) -20 cm

d) 20 cm

177 / 560

Category: Rules to Trace the Image Formed by Spherical Mirrors

177. (A) A virtual image is always formed on the same side of the mirror as the object in a convex mirror.
(R) In convex mirrors, the reflected rays diverge and appear to come from a point behind the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

178 / 560

Category: Virtual image: positive magnification.

178. (A) For a convex mirror, the magnification is always positive, regardless of the object's position.
(R) The image formed by a convex mirror is always virtual and erect.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

179 / 560

Category: Concave Mirror:

179. (A) A concave mirror always forms a real image.
(R) Concave mirrors converge light rays to a focal point.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

180 / 560

Category: Magnification

180. An object is placed at a distance of 20 cm from a concave mirror with a focal length of 10 cm. If the object moves towards the mirror at a speed of 2 cm/s, what is the speed of the image when the object is at 15 cm from the mirror?

a) 4 cm/s away from the mirror

b) 8 cm/s towards the mirror

c) 8 cm/s away from the mirror

d) 4 cm/s towards the mirror

181 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

181. Why is the aperture important in a spherical mirror?

a) It defines the mirror's focal length

b) It determines the mirror's magnification power

c) It specifies the mirror's radius of curvature

d) It determines the extent of the mirror that reflects light

182 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

182. (A) A convex mirror always forms a virtual, erect, and diminished image.
(R) The focal length of a convex mirror is positive and the image distance is always positive.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

183 / 560

Category: Introduction to Reflection

183. What is the relation between focal length ($f$) and radius of curvature ($R$) for a spherical mirror?

a) $f = R$

b) $f = \frac{R}{2}$

c) $f = 2R$

d) $f = \frac{1}{R}$

184 / 560

Category: Pole = origin, principal axis = X-axis.

184. An object is placed between the center of curvature ($C$) and the focus ($F$) of a concave mirror. Which statement about the image formed is correct?

a) Virtual, upright, and diminished

b) Real, inverted, and diminished

c) Real, inverted, and enlarged

d) Virtual, upright, and enlarged

185 / 560

Category: Shaving mirror

185. For a concave mirror used as a shaving mirror, if the object distance $u$ is less than the focal length $f$, what type of image is formed?

a) Real and inverted.

b) Virtual and inverted.

c) Real and erect.

d) Virtual and erect.

186 / 560

Category: Magnification

186. (A) The magnification produced by a convex mirror is always positive.
(R) A convex mirror always forms a virtual, erect image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

187 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

187. For an object placed at a finite distance from a convex mirror, what is the nature of the image formed?

a) Real, inverted, enlarged

b) Virtual, inverted, diminished

c) Virtual, erect, diminished

d) Real, erect, magnified

188 / 560

Category: Sign Conventions (New Cartesian)

188. (A) For a convex mirror, the focal length ($f$) is positive according to the New Cartesian Sign Convention.
(R) The New Cartesian Sign Convention states that distances measured along the principal axis to the right of the pole are taken as positive.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

189 / 560

Category: Concave Mirror:

189. What is the mirror formula for a concave mirror?

a) \$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\$

b) \$\frac{v}{u} = \frac{f}{v}\$

c) \$v + u = f\$

d) \$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\$

190 / 560

Category: Magnification

190. An object moves towards a concave mirror with velocity 5 m/s. If the magnification produced by the mirror is $-4$, what is the velocity of the image?

a) 20 m/s away from the mirror

b) 80 m/s away from the mirror

c) 20 m/s towards the mirror

d) 80 m/s towards the mirror

191 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

191. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 15 cm. What is the nature and position of the image formed?

a) Real, inverted, and formed at 20 cm

b) Virtual, erect, and formed at 60 cm

c) Real, inverted, and formed at 30 cm

d) Virtual, inverted, and formed at 45 cm

192 / 560

Category: Concave Mirror:

192. An object is placed 15 cm in front of a concave mirror with a focal length of 10 cm. What is the magnification of the image formed?

a) 0.5

b) 1.0

c) -2.0

d) 2.0

193 / 560

Category: Searchlights, headlights, solar cookers

193. Which of the following devices uses a concave mirror as a reflector?

a) Bicycle rear-view mirror

b) Solar cooker

c) Magnifying glass

d) Periscope

194 / 560

Category: Reflecting telescopes

194. What is the formula for calculating the magnification ($M$) of a reflecting telescope?

a) $M = f_o + f_e$

b) $M = f_o - f_e$

c) $M = \frac{f_e}{f_o}$

d) $M = \frac{f_o}{f_e}$

195 / 560

Category: Rules for Image Formation

195. A ray of light is incident on a concave mirror passing through its centre of curvature. What will be the path of the reflected ray?

a) It becomes parallel to the principal axis.

b) It diverges away from the principal axis.

c) It passes through the focus.

d) It returns back along the same path.

196 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

196. For a convex mirror, if the object distance is doubled, how does the image distance change assuming the focal length remains constant?

a) Image distance becomes half

b) Image distance doubles

c) Image distance increases but remains between P and F

d) Image distance decreases to zero

197 / 560

Category: Concave Mirror:

197. An object is placed at a distance of 20 cm from a concave mirror. The image formed is virtual and three times the size of the object. What is the focal length of the mirror?

a) 15 cm

b) 30 cm

c) -15 cm

d) -30 cm

198 / 560

Category: Identification of Mirrors

198. A mirror forms a virtual, erect, and diminished image of an object placed near it. What type of mirror is this?

a) Plane mirror

b) Concave mirror

c) Convex mirror

d) Parabolic mirror

199 / 560

Category: Concave Mirror:

199. An object is placed between the focus and the center of curvature of a concave mirror. Which statement about the image is correct?

a) The image is virtual and erect

b) The image is formed between $F$ and $C$

c) The image is real, inverted, and diminished

d) The image is real, inverted, and enlarged

200 / 560

Category: Pole (P) – Geometric center of the mirror.

200. A concave mirror with a focal length of 20 cm forms an image at a distance of 40 cm from the pole. If the object is moved such that the new image distance becomes 10 cm, what is the change in the position of the object relative to the pole?

a) Object moves 30 cm towards the pole

b) Object moves 60 cm away from the pole

c) Object moves 60 cm towards the pole

d) Object moves 20 cm away from the pole

201 / 560

Category: Real image: negative magnification.

201. A concave mirror with a focal length of $f = -12 \, \text{cm}$ forms a real image that is three times the size of the object. What is the object distance from the mirror?

a) $-8 \, \text{cm}$

b) $-12 \, \text{cm}$

c) $-16 \, \text{cm}$

d) $-20 \, \text{cm}$

202 / 560

Category: Virtual erect image same size → Plane

202. What is the magnification produced by a plane mirror?

a) Greater than 1

b) Less than 1

c) Equal to 1

d) Negative

203 / 560

Category: Relation Between Focal Length and Radius of Curvature

203. For a convex mirror with radius of curvature R, if a light ray makes an angle of 60° with the principal axis before reflection, what would be the approximate focal length for this non-paraxial ray? (Given: $\cos 60° = 0.5$)

a) $\frac{R}{4}$

b) $\frac{R}{2}$

c) $R$

d) $2R$

204 / 560

Category: Types of reflection: Regular and Diffuse

204. What distinguishes regular reflection from diffuse reflection?

a) Surface texture does not affect reflection type

b) Regular reflection requires a colored surface, whereas diffuse reflection requires a black surface

c) Regular reflection produces scattered rays, while diffuse reflection produces parallel rays

d) Regular reflection occurs on smooth surfaces, while diffuse reflection occurs on rough surfaces

205 / 560

Category: Paraxial Rays vs. Marginal Rays

205. Which of the following statements is true about paraxial rays?

a) They are far from the principal axis.

b) They obey the general formula $f = \frac{R}{2 \cos \theta}$.

c) They are only applicable for large aperture mirrors.

d) They lie close to the principal axis and simplify derivations.

206 / 560

Category: Reflecting telescopes

206. A reflecting telescope has a primary mirror with a focal length of 1200 mm and an eyepiece with a focal length of 20 mm. What is the magnification of the telescope?

a) 30

b) 40

c) 60

d) 80

207 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

207. Why is the aperture of a spherical mirror kept small compared to its radius of curvature?

a) To reduce the weight of the mirror

b) To make the mirror more durable

c) To ensure paraxial ray approximation

d) To minimize the production cost of the mirror

208 / 560

Category: Convex Mirror (Reflecting surface is outward)

208. An object is placed at a distance of 20 cm from a convex mirror with a focal length of 10 cm. Where is the image formed?

a) 5 cm in front of the mirror

b) 6.67 cm behind the mirror

c) 10 cm in front of the mirror

d) 15 cm behind the mirror

209 / 560

Category: Principal Axis – Line joining P and C.

209. Which of the following points lies on the principal axis of a concave mirror?

a) Any point behind the mirror

b) Only the pole (P)

c) Pole (P), focus (F), and center of curvature (C)

d) Only the center of curvature (C)

210 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

210. (A) When an object is placed beyond the centre of curvature (C) of a concave mirror, the image formed lies between C and the focus (F).
(R) The image formed is real, inverted, and diminished because the object distance ($u$) is greater than the radius of curvature (R), making the image distance ($v$) fall between R/2 (F) and R.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

211 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

211. If an object is placed 30 cm from a convex mirror with a focal length of 15 cm, what is the image distance $v$? (Use $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$)

a) -10 cm

b) 20 cm

c) 10 cm

d) -20 cm

212 / 560

Category: Searchlights, headlights, solar cookers

212. A searchlight uses a concave mirror with a focal length of 20 cm. If the light source is placed at its focus, what is the radius of curvature of the mirror?

a) 30 cm

b) 40 cm

c) 50 cm

d) 60 cm

213 / 560

Category: Spherical Mirrors

213. An object is placed at a distance of 20 cm from the focus of a concave mirror. The real image formed is at a distance of 5 cm from the other focus. What is the focal length of the mirror?

a) Distance of object from focus ($x_1$) = 20 cm

b) Distance of image from focus ($x_2$) = 5 cm \end{itemize} Using Newton's formula: $x_1 \times x_2 = f^2$ Substituting the given values: $20 \times 5 = f^2$ $100 = f^2$ $f = 10 \, \text{cm}$ Hence, the focal length is 10 cm.

c) 8 cm

d) 10 cm

e) 12 cm

f) 15 cm

214 / 560

Category: Pole = origin, principal axis = X-axis.

214. (A) The pole of a concave mirror is taken as the origin in the Cartesian sign convention.
(R) The principal axis is the straight line joining the pole and the center of curvature, extended on both sides.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

215 / 560

Category: Velocity of Image

215. An object is moving towards a concave mirror with velocity $V_{om}$. The image velocity $V_{im}$ is given by:

a) $V_{im} = m V_{om}$

b) $V_{im} = -m V_{om}$

c) $V_{im} = m^2 V_{om}$

d) $V_{im} = -m^2 V_{om}$

216 / 560

Category: Street lamps for wide area illumination

216. (A) A convex mirror is used in street lamps for wide-area illumination because it produces a divergent beam.
(R) The focal length of a convex mirror is directly proportional to its radius of curvature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

217 / 560

Category: Reflecting telescopes

217. What is the primary function of a concave mirror in a reflecting telescope?

a) Absorb all incoming light to prevent scattering.

b) Collect and focus light from distant objects.

c) Reflect light back to the eyepiece without focusing it.

d) Diffract light into multiple wavelengths for analysis.

218 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

218. (A) When an object is placed between the focus $F$ and the pole $P$ of a concave mirror, the image formed is virtual, erect, and magnified.
(R) The virtual image is formed due to the divergence of reflected rays that appear to come from behind the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

219 / 560

Category: Virtual image: positive magnification.

219. An object is placed 15 cm in front of a convex mirror with a focal length of 10 cm. What is the nature and magnification of the image formed?

a) Virtual, inverted, magnified

b) Real, inverted, diminished

c) Virtual, erect, diminished

d) Real, erect, magnified

220 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

220. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 10 cm. Where is the image formed?

a) 15 cm behind the mirror

b) 15 cm in front of the mirror

c) 30 cm behind the mirror

d) 20 cm in front of the mirror

221 / 560

Category: Concave Mirror:

221. A concave mirror has a radius of curvature of 60 cm. If an object is placed at 45 cm from the mirror, the nature and position of the image will be:

a) Virtual, erect, and enlarged

b) Real, inverted, and diminished

c) Real, inverted, and enlarged

d) No image is formed

222 / 560

Category: Rules for Image Formation

222. An object is placed between infinity and the pole of a convex mirror. What is the nature of the image formed?

a) Real, inverted, and enlarged.

b) Virtual, erect, and enlarged.

c) Virtual, erect, and diminished.

d) Real, inverted, and diminished.

223 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

223. (A) When an object is placed between the focus (F) and the pole (P) of a concave mirror, the image formed is virtual, erect, and magnified.
(R) The image distance ($v$) for this case is positive because the image is formed behind the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

224 / 560

Category: Relation Between Focal Length and Radius of Curvature

224. What is the sign of the radius of curvature (\$R\$) for a concave mirror?

a) Positive

b) Negative

c) Zero

d) Indeterminate

225 / 560

Category: Ray through focus → becomes parallel to axis.

225. A ray of light is incident on a concave mirror such that it passes through the focus before reflection. After reflection, the ray will:

a) Become perpendicular to the principal axis

b) Pass through the center of curvature

c) Retrace its original path

d) Become parallel to the principal axis

226 / 560

Category: Concave Mirror (Reflecting surface is inward)

226. If the focal length of a concave mirror is $-20$ cm and the object is placed at $-40$ cm from the mirror, what is the image distance $(v)$ using the mirror formula?

a) $-80$ cm

b) $-40$ cm

c) $-10$ cm

d) $-60$ cm

227 / 560

Category: Pole (P) – Geometric center of the mirror.

227. According to the New Cartesian Convention, where is the pole of a spherical mirror located?

a) At the center of curvature of the mirror

b) At the focus of the mirror

c) At the vertex or geometric center of the mirror's surface

d) Midway between the focus and center of curvature

228 / 560

Category: Pole = origin, principal axis = X-axis.

228. A concave mirror has a focal length of 15 cm. If the mirror's center of curvature lies to the right of the pole, what is the correct sign of the radius of curvature?

a) $R = +15$ cm

b) $R = -15$ cm

c) $R = +30$ cm

d) $R = -30$ cm

229 / 560

Category: Concave Mirror:

229. (A) When an object is placed at the center of curvature of a concave mirror, the image formed is real, inverted, and of the same size as the object.
(R) For a concave mirror, when the object is placed at the center of curvature ($u = R$), the image distance ($v$) equals the object distance ($u$) according to the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

230 / 560

Category: Principal Focus (F)

230. A concave mirror with a radius of curvature $R = 30 \text{ cm}$ is placed in front of a light source. What is the principal focus ($F$) of this mirror?

a) 7.5 cm behind the mirror

b) 7.5 cm in front of the mirror

c) 15 cm behind the mirror

d) 15 cm in front of the mirror

231 / 560

Category: Ray through center → retraces path.

231. What happens when a light ray passes through the center of curvature $C$ of a concave mirror?

a) The ray reflects parallel to the principal axis.

b) The ray retraces its path.

c) The ray diverges away from the principal axis.

d) The ray gets absorbed by the mirror.

232 / 560

Category: Radius of Curvature (R) – Distance PC.

232. A concave mirror has a radius of curvature of 40 cm. What is its focal length?

a) 10 cm

b) -20 cm

c) 20 cm

d) -10 cm

233 / 560

Category: Paraxial Rays vs. Marginal Rays

233. A spherical mirror of radius 20 cm is illuminated by a beam of light with an angle of incidence $\theta = 30^\circ$ for marginal rays. What is the effective focal length for these marginal rays?

a) 10 cm

b) 11.55 cm

c) 15 cm

d) 20 cm

234 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

234. For a concave mirror with focal length $-20$ cm, an object is placed at $-10$ cm (between F and P). Calculate the magnification.

a) 0.5

b) 1.0

c) 1.5

d) 2.0

235 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

235. An object is placed at 40 cm from a concave mirror with a focal length of 10 cm. Which of the following describes the image formed?

a) Real, inverted, and magnified

b) Virtual, erect, and diminished

c) Real, inverted, and diminished

d) Virtual, inverted, and magnified

236 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

236. An object is placed 15 cm from the pole of a concave mirror whose focal length is 30 cm. Where is the image formed?

a) 30 cm in front of the mirror

b) 15 cm behind the mirror

c) 30 cm behind the mirror

d) 15 cm in front of the mirror

237 / 560

Category: Ophthalmoscopes, ENT examinations

237. How does a doctor view the illuminated ear, nose, or throat during an ENT examination using a concave mirror?

a) By looking around the sides of the mirror

b) Through a hole at the center of the mirror

c) Using a secondary magnifying lens

d) Via a digital screen attached to the mirror

238 / 560

Category: Paraxial Rays vs. Marginal Rays

238. A spherical mirror has a large aperture. Which of the following statements is true regarding the rays incident on it?

a) Only paraxial rays are significant.

b) Both paraxial and marginal rays are significant.

c) Only marginal rays are significant.

d) Neither paraxial nor marginal rays are significant.

239 / 560

Category: Concave: f, R negative; Convex: f, R positive.

239. (A) For a concave mirror, the focal length (\$ f \$) is negative because its center of curvature lies on the same side as the reflected light.
(R) The radius of curvature (\$ R \$) for a concave mirror is negative as per the sign convention.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

240 / 560

Category: For real image: m is negative.

240. A concave mirror forms a real image with magnification $-2$. If the object distance is $20$ cm, what is the focal length of the mirror?

a) $-\frac{40}{3}$ cm

b) $10$ cm

c) $-10$ cm

d) $\frac{40}{3}$ cm

241 / 560

Category: Ray through center → retraces path.

241. A light ray is incident on a concave mirror of radius of curvature 20 cm such that it passes through the center of curvature. After reflection, what happens to the path of this ray?

a) The ray diverges away from the principal axis

b) The ray converges towards the focus

c) The ray retraces its path back along the same line

d) The ray becomes parallel to the principal axis

242 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

242. (A) For a concave mirror, if an object is placed beyond the center of curvature (C), the image formed will be real, inverted, and diminished.
(R) As the object moves from infinity towards the center of curvature (C), the image moves away from the focus and its size increases.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

243 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

243. (A) When an object is placed beyond the center of curvature (C) of a concave mirror, the image formed is real, inverted, and diminished.
(R) The image distance (v) for such a case lies between the focal length (f) and the center of curvature (C).

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

244 / 560

Category: Reflecting telescopes

244. A reflecting telescope has a primary mirror with radius of curvature 2.4 m and an eyepiece with focal length 12 mm. If the secondary mirror increases the effective focal length of the primary by 20\%, what is the total magnification produced?

a) 100

b) 120

c) 140

d) 160

245 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

245. When an object is placed between the center of curvature (\$C\$) and the principal focus (\$F\$) of a concave mirror, where is the image formed?

a) At the center of curvature (\$C\$)

b) Between \$C\$ and \$F\$

c) Beyond the center of curvature (\$C\$)

d) At infinity

246 / 560

Category: Concave: f, R negative; Convex: f, R positive.

246. A concave mirror has a radius of curvature of $-40$ cm. What is its focal length and the nature of its principal focus?

a) 15 cm, virtual focus

b) -20 cm, real focus

c) 20 cm, virtual focus

d) -15 cm, real focus

247 / 560

Category: Concave Mirror:

247. An object is placed at a distance of 20 cm from a concave mirror of focal length 10 cm. What is the nature and position of the image formed?

a) Real, inverted, and magnified, at 40 cm from the mirror

b) Virtual, erect, and diminished, at 6.67 cm from the mirror

c) Real, inverted, and same size, at 20 cm from the mirror

d) Virtual, erect, and magnified, at 10 cm from the mirror

248 / 560

Category: Laws of reflection

248. An object is placed in front of a plane mirror. If the distance between the object and the mirror is 10 cm, what will be the distance between the object and its image?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

249 / 560

Category: Reflecting telescopes

249. (A) A paraboloidal mirror is preferred over a spherical mirror in large reflecting telescopes because it eliminates spherical aberration for all incident rays parallel to the principal axis.
(R) Spherical mirrors exhibit spherical aberration where non-paraxial rays do not converge to a single focal point, unlike paraboloidal mirrors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

250 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

250. An object is placed at a finite distance from a convex mirror. Where will the image be formed?

a) Beyond the center of curvature

b) At the focus

c) Between the pole and the focus

d) At infinity

251 / 560

Category: Convex Mirror (Reflecting surface is outward)

251. What is the relationship between the focal length ($f$) and the radius of curvature ($R$) of a convex mirror?

a) $f = 2R$

b) $f = R$

c) $f = \frac{R}{2}$

d) $f = \frac{1}{R}$

252 / 560

Category: Pole (P) – Geometric center of the mirror.

252. According to the New Cartesian Sign Convention, how is the pole (P) treated?

a) As a point with no significance in sign convention

b) As the highest point on the mirror's surface

c) As the origin (0, 0) for measuring distances

d) As the focal point of the mirror

253 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

253. Which of the following statements correctly describes the focal plane in spherical mirrors?

a) The plane parallel to the principal axis and passing through the center of curvature.

b) The plane perpendicular to the principal axis and passing through the principal focus.

c) The plane tangent to the vertex of the mirror and parallel to the principal axis.

d) The plane containing the principal axis and the center of curvature.

254 / 560

Category: Ray parallel to axis → passes through focus.

254. In a concave mirror, if the distance of an object from the focus is 10 cm and the distance of its real image from the focus is 40 cm, what is the focal length of the mirror?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

255 / 560

Category: Pole (P) – Geometric center of the mirror.

255. A convex mirror has a radius of curvature of 30 cm. An object is placed at a distance of 45 cm from the pole. Where will the image be formed relative to the pole?

a) 5.25 cm behind the mirror

b) 7.50 cm behind the mirror

c) 10.00 cm behind the mirror

d) 11.25 cm behind the mirror

256 / 560

Category: Searchlights, headlights, solar cookers

256. A car headlight uses a paraboloidal concave mirror with a small bulb placed slightly away from its focus. What effect does this have on the beam of light produced?

a) The beam becomes more intense and narrower

b) The beam becomes less intense and wider

c) The beam remains perfectly parallel

d) The beam disappears completely

257 / 560

Category: Pole (P) – Geometric center of the mirror.

257. What is the pole of a spherical mirror?

a) The point where light rays converge after reflection

b) The central point of the reflecting surface of the mirror

c) The midpoint between the center of curvature and focus

d) The edge of the mirror's reflecting surface

258 / 560

Category: Ray obeys law of reflection at surface.

258. Where does the normal at any point on a spherical mirror lie?

a) Along the principal axis.

b) Perpendicular to the tangent at that point.

c) Along the line joining the point to the center of curvature.

d) Parallel to the incident ray.

259 / 560

Category: Principal Axis – Line joining P and C.

259. A concave mirror with a radius of curvature of $50 \, \text{cm}$ produces a sharp image of an object placed at infinity when only paraxial rays are considered. If the mirror is used to focus sunlight (which consists of both paraxial and marginal rays), where will the marginal rays converge compared to the paraxial rays?

a) At the same point as paraxial rays

b) Farther from the mirror than paraxial rays

c) Closer to the mirror than paraxial rays

d) Parallel to the principal axis

260 / 560

Category: Paraxial Rays vs. Marginal Rays

260. If in a concave mirror, the distance of an object from the focus is $x_1 = 4$ cm and the distance of its real image from the focus is $x_2$, what is $x_2$ if $f = 2$ cm? (Use Newton's formula)

a) 0.5 cm

b) 1 cm

c) 2 cm

d) 4 cm

261 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

261. A spherical mirror has a radius of curvature of 20 cm. What is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

262 / 560

Category: Introduction to Reflection

262. A ray of light is incident on a concave mirror parallel to its principal axis. After reflection, where does it pass through or appear to come from?

a) Centre of curvature

b) Pole of the mirror

c) Focus of the mirror

d) Infinity

263 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

263. (A) For a concave mirror, when the object is placed between C and F, the image formed is real, inverted, and enlarged.
(R) The image formed beyond C is real and inverted because the light rays actually converge at the image position.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

264 / 560

Category: Principal Focus (F)

264. The principal focus of a mirror is defined as:

a) The point where all light rays pass through after reflection.

b) The point on the principal axis where parallel rays meet or appear to come from after reflection.

c) The center of curvature of the mirror.

d) The vertex of the mirror.

265 / 560

Category: Rear-view mirrors in vehicles

265. An object is placed at a distance of 30 cm from a convex rear-view mirror with a focal length of 15 cm. Where is the image formed?

a) 5 cm behind the mirror

b) 10 cm behind the mirror

c) 15 cm behind the mirror

d) 20 cm behind the mirror

266 / 560

Category: Convex Mirror (Reflecting surface is outward)

266. An object is placed 25 cm in front of a convex mirror with a focal length of 10 cm. What is the magnification of the image formed?

a) 0.20

b) 0.29

c) 0.40

d) 0.50

267 / 560

Category: Virtual erect image same size → Plane

267. An object is placed 20 cm in front of a plane mirror. What is the magnification of the image formed?

a) $-1$

b) $+0.5$

c) $+1$

d) $+2$

268 / 560

Category: Street lamps for wide area illumination

268. Why are convex mirrors preferred over plane mirrors for street lighting applications?

a) They produce brighter light

b) They reflect light without any divergence

c) They spread light over a large area with a single lamp

d) They focus light at a single point

269 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

269. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 10 cm. What is the nature and position of the image formed?

a) Real, inverted, and at 15 cm from the mirror

b) Virtual, erect, and at 15 cm from the mirror

c) Real, inverted, and at 7.5 cm from the mirror

d) Virtual, erect, and at 7.5 cm from the mirror

270 / 560

Category: Virtual erect image same size → Plane

270. (A) A virtual image formed by a plane mirror cannot be projected onto a screen.
(R) The rays of light appear to diverge from the virtual image, making it impossible to capture on a screen.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

271 / 560

Category: Types of reflection: Regular and Diffuse

271. What happens during diffuse reflection?

a) Light reflects in a single direction

b) Light gets absorbed entirely

c) Light scatters in multiple random directions

d) Only some wavelengths of light are reflected

272 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

272. Where is the image formed when an object is placed at the centre of curvature ($C$) of a concave mirror?

a) At the focus ($F$)

b) Between $C$ and $F$

c) At infinity

d) At the centre of curvature ($C$)

273 / 560

Category: Virtual erect image same size → Plane

273. An object is placed in front of a mirror, and the image observed is virtual, erect, and of the same size as the object. What type of mirror is used?

a) Concave mirror

b) Convex mirror

c) Plane mirror

d) Parabolic mirror

274 / 560

Category: Ray obeys law of reflection at surface.

274. A ray of light strikes a plane mirror with an angle of incidence of 30 degrees. What is the angle between the reflected ray and the normal to the surface?

a) 15 degrees

b) 30 degrees

c) 45 degrees

d) 60 degrees

275 / 560

Category: Street lamps for wide area illumination

275. A convex mirror has a radius of curvature of 60 cm. If an object is placed at a distance of 15 cm from the mirror, what will be the position and nature of the image formed?

a) 10 cm, virtual and erect

b) 20 cm, real and inverted

c) 30 cm, virtual and erect

d) 40 cm, real and inverted

276 / 560

Category: Rules for Image Formation

276. A ray directed towards the focus of a convex mirror will, after reflection, become:

a) Converge at the center of curvature (C)

b) Reflect back along the same path

c) Diverge away from the principal axis

d) Parallel to the principal axis

277 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

277. (A) For an object placed at a finite distance from a convex mirror, the image is always virtual and erect.
(R) A convex mirror diverges incident rays, causing the reflected rays to appear to come from a point behind the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

278 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

278. What is the aperture of a spherical mirror?

a) The radius of curvature of the mirror

b) The focal length of the mirror

c) The diameter of the periphery of the mirror

d) The distance between the object and the mirror

279 / 560

Category: Numerical Problems

279. (A) A concave mirror of radius of curvature 20 cm forms a virtual image that is twice the size of the object. The object must be placed at 10 cm from the mirror.
(R) For a concave mirror, when the object is placed between the focus and the pole, the image formed is virtual, erect, and magnified.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

280 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

280. For an object placed anywhere in front of a convex mirror, which of the following statements about the image is always true?

a) It is real and inverted

b) It is virtual and diminished

c) It is real and magnified

d) It is virtual and magnified

281 / 560

Category: Convex Mirror (Reflecting surface is outward)

281. A convex mirror is used in a parking lot to monitor a wide area. If the mirror has a radius of curvature of 100 cm, where will the image of a car appear if the car is located 500 cm from the mirror?

a) 33.33 cm

b) 45.45 cm

c) 50.00 cm

d) 55.55 cm

282 / 560

Category: Virtual image: positive magnification.

282. (A) For a concave mirror, when an object is placed between the pole and focus, the magnification is greater than 1.
(R) The virtual image formed by a concave mirror in this case is enlarged and erect.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

283 / 560

Category: Pole (P) – Geometric center of the mirror.

283. Which statement correctly describes the position of the pole in both concave and convex mirrors?

a) The pole lies closer to the center of curvature in concave mirrors than in convex mirrors

b) The pole is present only in concave mirrors and not in convex mirrors

c) The pole is the midpoint of the principal axis in both types of mirrors

d) The pole is the central point of the reflecting surface in both concave and convex mirrors

284 / 560

Category: Image Formation by Spherical Mirrors

284. A convex mirror always forms which type of image?

a) Real and inverted

b) Virtual and erect

c) Real and erect

d) Virtual and inverted

285 / 560

Category: Principal Focus (F)

285. The principal focus of a convex mirror is:

a) Real and lies in front of the mirror.

b) Virtual and lies in front of the mirror.

c) Real and lies behind the mirror.

d) Virtual and lies behind the mirror.

286 / 560

Category: Shaving mirror

286. A concave mirror with a focal length of 30 cm is used as a shaving mirror. If the magnification produced is 4, at what distance should the face be placed from the mirror?

a) 22.5 cm

b) 25.0 cm

c) 18.5 cm

d) 15.0 cm

287 / 560

Category: Rules to Trace the Image Formed by Spherical Mirrors

287. (A) A ray of light parallel to the principal axis after reflection from a concave mirror passes through its focus.
(R) The focus is the point where all parallel rays converge after reflection.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

288 / 560

Category: Ray parallel to axis → passes through focus.

288. If an object is placed at a distance $x_1$ from the focus of a concave mirror and forms a real image at a distance $x_2$, what is the relation between $x_1$, $x_2$, and the focal length $f$?

a) $x_1 + x_2 = f$

b) $x_1 x_2 = f^2$

c) $x_1 - x_2 = f$

d) $\frac{x_1}{x_2} = f$

289 / 560

Category: Introduction to Reflection

289. A concave mirror has a focal length of 20 cm. If an object is placed at a distance of 30 cm from the mirror, what is the position of the image formed?

a) 30 cm behind the mirror

b) 60 cm behind the mirror

c) 30 cm in front of the mirror

d) 60 cm in front of the mirror

290 / 560

Category: Derived for both Concave and Convex mirrors

290. If an object is placed between the focus and the pole of a concave mirror, the nature of the image formed is:

a) Real and inverted

b) Virtual and diminished

c) Virtual and erect

d) Real and erect

291 / 560

Category: Shaving mirror

291. If a concave mirror has a focal length of 36 cm, at what distance should an object be placed to get an upright image with a magnification of 4?

a) 18 cm from the mirror

b) 27 cm from the mirror

c) 45 cm from the mirror

d) 9 cm from the mirror

292 / 560

Category: Shaving mirror

292. (A) A concave mirror with a focal length of 0.4 m produces an erect image with a magnification of 5 when used for shaving.
(R) The object must be placed within the focal length of the concave mirror to achieve an erect and magnified virtual image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

293 / 560

Category: Ray through center → retraces path.

293. A non-paraxial ray passes through the center of curvature of a concave mirror with a large aperture. How does the reflected ray behave compared to a paraxial ray under similar conditions?

a) It retraces its path exactly like the paraxial ray

b) It reflects parallel to the principal axis

c) It deviates slightly and does not retrace its path exactly

d) It converges towards the focus instead

294 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

294. For an object placed between the focus (F) and the pole (P) of a concave mirror, the magnification ($m$) is given by:

a) $m = \frac{u}{v}$

b) $m = -\frac{v}{u}$

c) $m = \frac{v}{u}$

d) $m = -\frac{u}{v}$

295 / 560

Category: Concave: f, R negative; Convex: f, R positive.

295. If the radius of curvature (\$R\$) of a convex mirror is +20 cm, what is its focal length (\$f\$)?

a) 40 cm

b) -10 cm

c) 10 cm

d) -5 cm

296 / 560

Category: Reflecting telescopes

296. In a Cassegrain telescope configuration, how does the light path differ from the Newtonian design?

a) Light reflects twice before exiting through the side

b) Light exits through a hole in the primary mirror

c) Uses a concave secondary mirror

d) Requires no secondary mirror

297 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

297. For a concave mirror with radius of curvature 40 cm, an object placed between C and F gives an image magnification of -2. What was the object distance?

a) 15 cm

b) 20 cm

c) 25 cm

d) 30 cm

298 / 560

Category: For real image: m is negative.

298. A small object is placed along the principal axis of a convex mirror with a focal length of 15 cm. If the object moves from 30 cm to 20 cm away from the mirror, what is the change in the image's size? Assume the object size is negligible.

a) Increase by about 9.5\%

b) Decrease by about 4.8\%

c) No change

d) Increase by about 19.0\%

299 / 560

Category: Concave: f, R negative; Convex: f, R positive.

299. A convex mirror always forms:

a) Real and inverted images

b) Virtual and erect images

c) Enlarged and real images

d) Inverted and enlarged images

300 / 560

Category: Spherical Mirrors

300. Which of the following is NOT a common use of a convex mirror?

a) Reflector in street lamps

b) Driver's mirror in cars

c) Shaving mirror

d) Security mirrors in stores

301 / 560

Category: Principal Focus (F)

301. The focal length ($f$) of a concave mirror is 10 cm. How far is the principal focus ($F$) from the pole of the mirror?

a) 5 cm

b) 10 cm

c) 20 cm

d) 40 cm

302 / 560

Category: Identification of Mirrors

302. A virtual image larger than the object can be produced by:

a) concave mirror

b) convex mirror

c) plane mirror

d) none of these

303 / 560

Category: Concave Mirror (Reflecting surface is inward)

303. A concave mirror forms a virtual image with magnification $+3$. If the object distance is $-10$ cm, what is the image distance?

a) $15$ cm

b) $-30$ cm

c) $30$ cm

d) $-15$ cm

304 / 560

Category: Image Formation by Spherical Mirrors

304. Which ray retraces its path after reflection from a concave mirror?

a) Ray parallel to the principal axis

b) Ray passing through the focus

c) Ray directed towards the pole

d) Ray passing through the center of curvature

305 / 560

Category: Mirror Formula

305. What is the magnification ($m$) formula for a spherical mirror in terms of object distance ($u$) and image distance ($v$)?

a) $m = v \times u$

b) $m = \frac{u}{v}$

c) $m = -\frac{u}{v}$

d) $m = -\frac{v}{u}$

306 / 560

Category: Radius of Curvature (R) – Distance PC.

306. If the angle of incidence $\theta$ of a light ray on a spherical mirror is 30°, and the radius of curvature $R$ is 40 cm, what is the approximate focal length using the general formula?

a) 20 cm

b) 23.09 cm

c) 25 cm

d) 28 cm

307 / 560

Category: Ophthalmoscopes, ENT examinations

307. If the image distance ($v$) in an ENT examination using a concave mirror is 10 cm and the object distance ($u$) is 5 cm, what is the magnification ($m$)?

a) 0.5

b) 1.0

c) 1.5

d) 2.0

308 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

308. An object is placed beyond the center of curvature $C$ of a concave mirror. What is the nature and position of the image formed?

a) Real, erect, enlarged

b) Virtual, inverted, diminished

c) Real, inverted, diminished

d) Virtual, erect, magnified

309 / 560

Category: Concave Mirror (Reflecting surface is inward)

309. An object is placed between the focus and the pole of a concave mirror. Which of the following statements about the image is correct?

a) Real and inverted

b) Virtual and inverted

c) Virtual and erect

d) Real and erect

310 / 560

Category: Virtual image: positive magnification.

310. A concave mirror has a focal length of 20 cm. If an object is placed at 15 cm from the mirror, what will be the magnification of the image formed?

a) -4

b) 4

c) 0.25

d) -0.25

311 / 560

Category: Uses of Spherical Mirrors

311. Which mirror is used in vehicles to observe traffic at the back and why?

a) Concave mirror, as it magnifies the image.

b) Plane mirror, as it gives a clear image.

c) Convex mirror, as it provides a wider field of view.

d) Concave mirror, as it provides a narrower field of view.

312 / 560

Category: Pole (P) – Geometric center of the mirror.

312. Which of the following is true about the pole in the mirror formula ($\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$)?

a) It represents the focal length of the mirror

b) It is used as the reference point for measuring distances

c) It determines whether the mirror is concave or convex

d) It is only relevant for convex mirrors

313 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

313. A convex mirror has a focal length of 10 cm. If an object is placed 20 cm from the mirror, what is the image distance ($v$)? Use the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.

a) -6.67 cm

b) 6.67 cm

c) -20 cm

d) 10 cm

314 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

314. A concave mirror produces an image twice as large as the object when the object is placed between C and F. If the image distance is 45 cm, what is the radius of curvature of the mirror?

a) 20 cm

b) 30 cm

c) 40 cm

d) 45 cm

315 / 560

Category: Ray obeys law of reflection at surface.

315. A paraxial ray is incident on a convex mirror. If the angle of incidence is $10^\circ$, what will be the angle of reflection according to the law of reflection?

a) 5 degrees

b) 10 degrees

c) 20 degrees

d) 40 degrees

316 / 560

Category: Concave Mirror:

316. A concave mirror forms an image that is twice the size of the object. If the object distance is 20 cm, what is the focal length of the mirror?

a) 13.3 cm

b) -13.3 cm

c) 40 cm

d) -40 cm

317 / 560

Category: Definition of Reflection

317. Which combination of two rays can uniquely determine the position and nature of an image formed by a concave mirror when the object is placed beyond the centre of curvature?

a) A ray through $F$ and a ray striking the pole

b) A parallel ray and a ray through $C$

c) A ray through $F$ and a perpendicular ray

d) A parallel ray and a ray striking the pole

318 / 560

Category: Derived for both Concave and Convex mirrors

318. What is the radius of curvature for a convex mirror with a focal length of 15 cm?

a) 7.5 cm

b) 15 cm

c) 30 cm

d) 45 cm

319 / 560

Category: Reflecting telescopes

319. Which of the following statements correctly explains why reflecting telescopes are preferred over refracting telescopes for astronomical observations?

a) Mirrors are easier to clean than lenses

b) Reflecting telescopes produce upright images

c) Mirrors can correct both chromatic and spherical aberration

d) Reflecting telescopes eliminate chromatic aberration and allow larger apertures

320 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

320. An object is placed off-axis above the principal axis of a concave mirror. Where will its image be located with respect to the focal plane?

a) On the principal axis below the focal plane.

b) At the center of curvature.

c) Somewhere on the focal plane.

d) Beyond the focal plane, behind the mirror.

321 / 560

Category: Ray through focus → becomes parallel to axis.

321. A concave mirror has a radius of curvature $R$. If a ray passes through its focus and reflects off the mirror, how is the focal length ($f$) related to the radius of curvature?

a) $f = R$

b) $f = 2R$

c) $f = \frac{R}{3}$

d) $f = \frac{R}{2}$

322 / 560

Category: few Definitions Regarding Spherical Mirrors

322. An object is placed at a distance equal to twice the focal length from a concave mirror. What will be the ratio of the image distance to the radius of curvature of the mirror?

a) $\frac{1}{4}$

b) $\frac{1}{3}$

c) $\frac{1}{2}$

d) $\frac{2}{3}$

323 / 560

Category: Mirror Formula

323. An object is placed 30 cm from a concave mirror with a focal length of 10 cm. What is the image distance?

a) 30 cm

b) -15 cm

c) 15 cm

d) -30 cm

324 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

324. According to Newton's formula for a concave mirror, if the distance of an object from the focus is $x_1$ and the distance of its real image is $x_2$, what is the relation between $x_1$, $x_2$, and $f$?

a) $x_1 + x_2 = f$

b) $x_1 - x_2 = f$

c) $x_1 x_2 = f^2$

d) $\frac{x_1}{x_2} = f$

325 / 560

Category: Sign Conventions (New Cartesian)

325. (A) For a convex mirror, if the object is placed at a distance of 20 cm from the pole, the image formed will always have a positive image distance.
(R) According to the New Cartesian Sign Convention, the focal length of a convex mirror is positive and all virtual images formed by it have positive image distances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

326 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

326. An object is placed between the focus (F) and pole (P) of a concave mirror. If the magnification produced by the mirror is 3, what is the ratio of the image distance to the focal length?

a) $\frac{2}{3}$

b) $-2$

c) $\frac{1}{3}$

d) $-3$

327 / 560

Category: Definition of Reflection

327. An object is placed 20 cm in front of a concave mirror with a focal length of 10 cm. What is the nature and position of the image formed?

a) Real, 20 cm in front of the mirror

b) Virtual, 20 cm behind the mirror

c) Real, 10 cm in front of the mirror

d) Virtual, 10 cm behind the mirror

328 / 560

Category: Principal Axis – Line joining P and C.

328. All distances in spherical mirrors are measured along the principal axis from which point?

a) Option 1: From the center of curvature (C)

b) Option 2: From the focus (F)

c) Option 3: From the pole (P)

d) Option 4: From the midpoint between P and C

329 / 560

Category: Ray parallel to axis → passes through focus.

329. A ray of light is incident parallel to the principal axis of a convex mirror. After reflection, what happens to the ray?

a) It passes through the principal focus

b) It appears to diverge from the principal focus

c) It reflects back along its original path

d) It meets the principal axis at infinity

330 / 560

Category: Convex Mirror (Reflecting surface is outward)

330. The radius of curvature of a convex mirror is 30 cm. What is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

331 / 560

Category: Ray through center → retraces path.

331. A ray of light is incident towards the center of curvature $C$ of a concave mirror. After reflection, the path of the ray will:

a) Pass through the focus

b) Retrace its original path

c) Become parallel to the principal axis

d) Diverge away from the principal axis

332 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

332. An object is placed 40 cm in front of a convex mirror with focal length 20 cm. Which statement about the image is correct?

a) Image is real and magnified

b) Image is virtual and same size

c) Image is real and inverted

d) Image is virtual and diminished

333 / 560

Category: Spherical Mirrors

333. A convex mirror has a focal length of 12 cm. If an object is placed 24 cm in front of the mirror, find the distance of the image from the pole of the mirror.

a) Focal length ($f$) = +12 cm (positive for convex mirror)

b) Object distance ($u$) = -24 cm (negative as per sign convention) \end{itemize} Using the mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ Substitute the known values: $\frac{1}{12} = \frac{1}{v} + \frac{1}{-24}$ $\frac{1}{v} = \frac{1}{12} + \frac{1}{24}$ $\frac{1}{v} = \frac{2 + 1}{24} = \frac{3}{24} = \frac{1}{8}$ $v = 8 \, \text{cm}$ The positive sign indicates the image is virtual and located 8 cm behind the mirror.

c) 6 cm

d) 8 cm

e) 10 cm

f) 12 cm

334 / 560

Category: Principal Axis – Line joining P and C.

334. Which of the following correctly defines the principal axis in a spherical mirror?

a) Option 1: Line joining the pole (P) and the focal point (F)

b) Option 2: Line perpendicular to the mirror's surface at the pole (P)

c) Option 3: Line joining the pole (P) and any point on the mirror's periphery

d) Option 4: Line joining the pole (P) and the center of curvature (C)

335 / 560

Category: few Definitions Regarding Spherical Mirrors

335. If the radius of curvature of a concave mirror is 20 cm, what is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

336 / 560

Category: Sign Conventions (New Cartesian)

336. (A) In the New Cartesian sign convention, the focal length of a convex mirror is positive.
(R) The positive focal length indicates that the focus lies on the right side of the pole along the $+X$-axis for a convex mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

337 / 560

Category: Definition of Reflection

337. Which of the following statements about convex mirrors is correct?

a) The image formed is always real and inverted.

b) The image can be magnified depending on the object distance.

c) The image is always virtual, erect, and diminished.

d) It converges parallel rays to a focus.

338 / 560

Category: Pole = origin, principal axis = X-axis.

338. (A) In a concave mirror, if the object is placed at a distance of 20 cm to the left of the pole, then the image formed will also be located to the left of the pole.
(R) According to the sign conventions, distances measured to the left of the pole are negative.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

339 / 560

Category: Identification of Mirrors

339. (A) A concave mirror always forms a real and inverted image for an object placed beyond its focal length.
(R) For a concave mirror, when the object is placed between the focal point and the center of curvature, the image is real, inverted, and magnified.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

340 / 560

Category: Virtual erect image same size → Plane

340. If an object placed in front of a mirror produces a virtual, erect, and same-sized image, which formula correctly represents the relationship between object distance ($u$) and image distance ($v$)?

a) $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

b) $v = u$

c) $v = -u$

d) $v = 2u$

341 / 560

Category: Real image: negative magnification.

341. An object is placed in front of a concave mirror such that the magnification produced is $-3$. What can be inferred about the nature of the image?

a) Virtual, erect, and diminished

b) Real, inverted, and diminished

c) Real, inverted, and magnified

d) Virtual, erect, and magnified

342 / 560

Category: Sign Conventions (New Cartesian)

342. An object is placed 20 cm in front of a concave mirror with a focal length of -15 cm. What is the distance of the image formed?

a) -30 cm

b) -40 cm

c) -50 cm

d) -60 cm

343 / 560

Category: Ray parallel to axis → passes through focus.

343. A ray of light parallel to the principal axis is incident on a convex mirror. After reflection, how does the reflected ray appear?

a) It passes through the focus

b) It appears to come from the focus

c) It returns along the same path

d) It becomes parallel to the principal axis again

344 / 560

Category: Ray through focus → becomes parallel to axis.

344. A ray of light is incident on a concave mirror such that it passes through the focus before striking the mirror. What will be the path of the reflected ray?

a) The ray will diverge away from the principal axis.

b) The ray will converge towards the principal axis.

c) The ray will become parallel to the principal axis.

d) The ray will retrace its original path.

345 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

345. What is the aperture of a mirror?

a) The distance from the mirror's pole to its center of curvature

b) The diameter of the periphery of the mirror

c) The focal length of the mirror

d) The radius of curvature of the mirror

346 / 560

Category: Ray diagrams for various object positions.

346. (A) For a concave mirror, if an object is placed between the focus (\$F\$) and the pole (\$P\$), the image formed is virtual and erect.
(R) The rays appear to diverge from a point behind the mirror when the object is placed between \$F\$ and \$P\$ in a concave mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

347 / 560

Category: Magnification

347. (A) The magnification produced by a concave mirror is negative when the image formed is real and inverted.
(R) For a concave mirror, a negative magnification indicates that the image is formed on the same side as the object.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

348 / 560

Category: Mirror Formula

348. An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. What is the magnification produced by the mirror?

a) 0.25

b) 0.50

c) 0.75

d) 1.00

349 / 560

Category: Ray diagrams for various object positions.

349. (A) For a concave mirror, when the object is placed at infinity, the image is formed at the focus.
(R) Rays parallel to the principal axis converge at the focus after reflection from a concave mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

350 / 560

Category: For real image: m is negative.

350. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 10 cm. If the image formed is real and inverted, what is the magnification produced by the mirror?

a) $-0.5$

b) $-1.5$

c) $-2.0$

d) $-0.33$

351 / 560

Category: Coordinate Geometry Sign Convention for Measuring Distances and Lengths

351. (A) For a convex mirror, the focal length ($f$) is positive.
(R) In the New Cartesian Convention, distances measured to the right of the pole are taken as positive, and the focus of a convex mirror lies on the right side.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

352 / 560

Category: Laws of reflection

352. A convex mirror has a radius of curvature of 40 cm. If an object is placed 20 cm from the mirror, which ray correctly describes the path of the reflected ray parallel to the principal axis?

a) Passes through the focus

b) Retraces its path

c) Appears to come from the focus

d) Reflects back parallel to the principal axis

353 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

353. A concave mirror has a focal length of 15 cm. A ray parallel to the principal axis but 5 cm away from it is incident on the mirror. Where does this ray intersect the focal plane after reflection?

a) At the focus $F$

b) 5 cm away from $F$ along the principal axis

c) 5 cm away from $F$ perpendicular to the principal axis in the focal plane

d) 10 cm away from $F$ perpendicular to the principal axis in the focal plane

354 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

354. An object is placed at a distance of 20 cm from a convex mirror with a focal length of 10 cm. Where will the image be formed and what will be its nature?

a) At 10 cm, real and inverted

b) At 6.67 cm, virtual and erect

c) At 20 cm, real and enlarged

d) At 15 cm, virtual and inverted

355 / 560

Category: Radius of Curvature (R) – Distance PC.

355. A convex mirror has a focal length of 12 cm. What is its radius of curvature?

a) 6 cm

b) 12 cm

c) 24 cm

d) 48 cm

356 / 560

Category: Ray parallel to axis → passes through focus.

356. A ray of light is incident parallel to the principal axis of a concave mirror. After reflection, where does the ray pass through?

a) The center of curvature

b) The principal focus

c) The pole of the mirror

d) The midpoint of the focal length

357 / 560

Category: Derived for both Concave and Convex mirrors

357. For a concave mirror, if an object placed 10 cm from the focus produces a real image 40 cm from the other side of focus. What is the radius of curvature of the mirror?

a) 20 cm

b) 30 cm

c) 40 cm

d) 50 cm

358 / 560

Category: Uses of Spherical Mirrors

358. A convex mirror with a radius of curvature of 40 cm forms an image of an object placed 30 cm in front of it. What is the magnification of the image?

a) 0.5

b) 0.4

c) 0.6

d) 0.8

359 / 560

Category: Searchlights, headlights, solar cookers

359. If the radius of curvature ($R$) of a concave spherical mirror is 20 cm, what is its focal length ($f$)?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

360 / 560

Category: Ray through focus → becomes parallel to axis.

360. In a concave mirror, a ray passing through the focus will, after reflection:

a) Converge at the center of curvature

b) Diverge away from the principal axis

c) Become parallel to the principal axis

d) Reflect back along the same path

361 / 560

Category: Definition of Reflection

361. A light ray strikes a plane mirror at an angle of incidence of $30^\circ$. What will be the angle between the incident and reflected rays?

a) $30^\circ$

b) $45^\circ$

c) $60^\circ$

d) $90^\circ$

362 / 560

Category: Identification of Mirrors

362. An object is moved from infinity towards the pole of a convex mirror. What happens to the image?

a) Changes from real to virtual

b) Changes from inverted to erect

c) Decreases in size continuously

d) Increases in size continuously while remaining virtual and erect

363 / 560

Category: Sign Conventions (New Cartesian)

363. In a concave mirror, if the object is placed at a distance of 10 cm from the focus and the image formed is real and at a distance of 40 cm from the focus, what is the focal length of the mirror?

a) 10 cm

b) 20 cm

c) -10 cm

d) -20 cm

364 / 560

Category: Magnification

364. A concave mirror produces a virtual image with magnification +3. What does the positive sign indicate?

a) Image is real and inverted

b) Image is virtual and inverted

c) Image is real and erect

d) Image is virtual and erect

365 / 560

Category: Real image: negative magnification.

365. A concave mirror with a radius of curvature 40 cm forms a real image twice the size of the object. Where is the object placed?

a) 10 cm from the mirror

b) 20 cm from the mirror

c) 30 cm from the mirror

d) 40 cm from the mirror

366 / 560

Category: Uses of Spherical Mirrors

366. (A) A concave mirror is used by ENT doctors to examine the ear, nose, and throat.
(R) A concave mirror reflects a convergent beam of light, which helps in illuminating the internal organs clearly.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

367 / 560

Category: Principal Focus (F)

367. Which of the following correctly describes the principal focus $(F)$ of a convex mirror with a focal length of $-20 \text{ cm}$?

a) Real and located 20 cm in front of the mirror

b) Virtual and located 20 cm in front of the mirror

c) Real and located 20 cm behind the mirror

d) Virtual and located 20 cm behind the mirror

368 / 560

Category: Pole (P) – Geometric center of the mirror.

368. All the following distances are measured from the pole of a spherical mirror except:

a) Object distance ($u$)

b) Image distance ($v$)

c) Focal length ($f$)

d) Diameter of the mirror

369 / 560

Category: Laws of reflection

369. For a concave mirror, if the distance of an object from the focus is 10 cm and the focal length is 15 cm, what is the distance of the real image from the focus?

a) 15 cm

b) 20 cm

c) 22.5 cm

d) 25 cm

370 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

370. Where is the image located when an object is placed at a finite distance from a convex mirror?

a) Beyond the center of curvature

b) At the focus

c) Between P and F

d) At infinity

371 / 560

Category: For real image: m is negative.

371. An object is placed in front of a concave mirror such that the magnification is $-0.5$. Which of the following statements is correct?

a) The image is virtual and magnified

b) The image is real and erect

c) The image is real, inverted, and diminished

d) The image is virtual and inverted

372 / 560

Category: At finite distance → Between P & F, virtual, erect, diminished.

372. (A) For an object placed at a finite distance from a convex mirror, the image formed is always real and inverted.
(R) The mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ for a convex mirror always yields a positive image distance $v$ due to its diverging nature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

373 / 560

Category: Ophthalmoscopes, ENT examinations

373. (A) A concave mirror is used in an ophthalmoscope to reflect light onto the retina of the eye.
(R) The converging property of a concave mirror ensures focused illumination for better visibility.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

374 / 560

Category: Concave Mirror (Reflecting surface is inward)

374. An object is placed between the focus $F$ and the center of curvature $C$ of a concave mirror. What is the magnification of the image formed?

a) Less than 1 and positive

b) Greater than 1 and positive

c) Less than 1 and negative

d) Greater than 1 and negative

375 / 560

Category: Magnification

375. A concave mirror of focal length 20 cm forms an image that is twice the size of the object. What is the object distance if the image is real?

a) Object is placed at 10 cm from the mirror

b) Object is placed at 20 cm from the mirror

c) Object is placed at 30 cm from the mirror

d) Object is placed at 40 cm from the mirror

376 / 560

Category: Velocity of Image

376. An object is moving perpendicular to the principal axis of a concave mirror with velocity $V_{om}$. The image velocity $V_{im}$ in this case is:

a) $V_{im} = -m^2 V_{om}$

b) $V_{im} = m^2 V_{om}$

c) $V_{im} = -m V_{om}$

d) $V_{im} = m V_{om}$

377 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

377. As an object moves from infinity towards the centre of curvature of a concave mirror, how does the image change?

a) Image changes from virtual to real and inverted

b) Image remains virtual and erect throughout

c) Image changes from real, inverted, and diminished to real, inverted, and enlarged

d) Image changes from real, inverted, and diminished to virtual and erect

378 / 560

Category: For real image: m is negative.

378. An object moves towards a concave mirror of focal length 20 cm with a velocity of 5 cm/s. At the instant when the object is 60 cm from the mirror, what is the velocity of the real image formed?

a) $-1.25$ cm/s

b) $-2.50$ cm/s

c) $-0.83$ cm/s

d) $-5.00$ cm/s

379 / 560

Category: Mirror Formula

379. (A) The mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ is valid only for paraxial rays.

(R) For large aperture mirrors, spherical aberration causes deviation from the mirror formula.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

380 / 560

Category: Derived for both Concave and Convex mirrors

380. An object is placed 20 cm in front of a convex mirror with a focal length of 10 cm. What is the nature of the image formed?

a) Real, inverted, enlarged

b) Virtual, inverted, diminished

c) Virtual, erect, diminished

d) Real, erect, enlarged

381 / 560

Category: Derived for both Concave and Convex mirrors

381. An object is placed at a distance of 30 cm from a convex mirror with focal length 20 cm. If the image formed is virtual and erect, what is the magnification produced?

a) 0.4

b) 0.6

c) 0.8

d) 1.2

382 / 560

Category: few Definitions Regarding Spherical Mirrors

382. What is the term used for the central point of the reflecting surface of a spherical mirror?

a) Principal axis

b) Centre of curvature

c) Radius of curvature

d) Pole

383 / 560

Category: Definition of Reflection

383. What is the phenomenon called when light, after striking a surface, returns back into the same medium?

a) Refraction

b) Diffraction

c) Reflection

d) Dispersion

384 / 560

Category: few Definitions Regarding Spherical Mirrors

384. In an experiment with a concave mirror, when an object is placed at a distance of 40 cm from the mirror, a real image is formed at 20 cm. If the object is now moved to a new position such that its distance from the focus becomes 5 cm, what will be the new image distance using Newton's formula?

a) 10 cm

b) 24 cm

c) 35 cm

d) 49 cm

385 / 560

Category: Real image: negative magnification.

385. (A) Real images have negative magnification.
(R) Negative magnification indicates that the image is inverted.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

386 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

386. A telescope uses a concave mirror with an effective aperture diameter of 8 cm. By how much does the light-gathering power increase if the aperture diameter is doubled while keeping all other parameters constant?

a) It doubles.

b) It increases by a factor of 4.

c) It remains the same.

d) It increases by a factor of 8.

387 / 560

Category: Concave: f, R negative; Convex: f, R positive.

387. A convex mirror has a radius of curvature of 30 cm. If a non-paraxial ray strikes the mirror at an angle of incidence of 60 degrees, what is the focal length for this ray?

a) 15 cm

b) 30 cm

c) 7.5 cm

d) 60 cm

388 / 560

Category: Image Formation by Spherical Mirrors

388. (A) A convex mirror always forms a virtual and erect image regardless of the position of the object.
(R) The reflected rays from a convex mirror diverge and appear to come from a point behind the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

389 / 560

Category: Ophthalmoscopes, ENT examinations

389. (A) Concave mirrors are used in ophthalmoscopes to examine the retina of the eye.
(R) Concave mirrors can form an enlarged virtual image when the object is placed between the pole and the focus.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

390 / 560

Category: Concave: f, R negative; Convex: f, R positive.

390. (A) For a concave mirror, the focal length ($f$) and radius of curvature ($R$) are both negative.
(R) This is because the principal focus ($F$) and center of curvature ($C$) lie on the same side as the incident light for a concave mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

391 / 560

Category: Image Formation by Spherical Mirrors

391. (A) For a concave mirror, if the object is placed at a distance equal to twice the focal length from the pole, then according to Newton’s formula, the image distance from the focus will be equal to the focal length.
(R) Newton’s formula states that for a concave mirror, the product of the object distance from the focus ($x_1$) and the image distance from the focus ($x_2$) is equal to the square of the focal length ($f$), i.e., $x_1 x_2 = f^2$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

392 / 560

Category: Laws of reflection

392. A light ray is incident on a plane mirror such that the angle between the incident ray and the mirror surface is $40^\circ$. What is the angle of deviation for this ray after reflection?

a) $50^\circ$

b) $80^\circ$

c) $100^\circ$

d) $120^\circ$

393 / 560

Category: Concave Mirror (Reflecting surface is inward)

393. A concave mirror has a focal length of 15 cm. An object is placed at a distance of 30 cm from the mirror. Where will the image be formed and what will be its nature?

a) At 30 cm, virtual and erect

b) At 30 cm, real and inverted

c) At 15 cm, virtual and erect

d) At 15 cm, real and inverted

394 / 560

Category: Concave Mirror (Reflecting surface is inward)

394. An object is placed at the center of curvature ($C$) of a concave mirror. What is the nature and position of the image formed?

a) Virtual, erect, and magnified

b) Real, inverted, and smaller than the object

c) Real, inverted, and equal in size

d) Virtual, erect, and same size as the object

395 / 560

Category: Real image: negative magnification.

395. For a concave mirror with focal length $f$, if the object is placed at a distance $2f$, where is the image formed?

a) At $f$

b) At $2f$ behind the mirror

c) At infinity

d) At $2f$ in front of the mirror

396 / 560

Category: Sign Conventions (New Cartesian)

396. A real image formed by a concave mirror has a height of 4 cm while the object height is 2 cm. If the image is located at 24 cm from the mirror, what is the position of the object and the mirror's radius of curvature?

a) Object distance = $-6$ cm, Radius of curvature = $-12$ cm

b) Object distance = $-12$ cm, Radius of curvature = $-16$ cm

c) Object distance = $-8$ cm, Radius of curvature = $-12$ cm

d) Object distance = $-24$ cm, Radius of curvature = $-48$ cm

397 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

397. Where is the image located when an object is placed between the focus (F) and the pole (P) of a concave mirror?

a) Between F and C (center of curvature)

b) Beyond C (center of curvature)

c) At infinity

d) Behind the mirror

398 / 560

Category: Ray through focus → becomes parallel to axis.

398. (A) A ray incident on a concave mirror after passing through its focus will, upon reflection, emerge parallel to the principal axis.
(R) The laws of reflection state that the angle of incidence equals the angle of reflection, which causes this behavior in both concave and convex mirrors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

399 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

399. A spherical mirror deviates from the standard relation $f = \frac{R}{2}$ for a light ray incident at an angle $\theta = 30^\circ$. What is the modified focal length if the radius of curvature $R$ is 50 cm?

a) 25 cm

b) 28.87 cm

c) 32.25 cm

d) 14.43 cm

400 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

400. An object is placed 60 cm in front of a concave mirror with a focal length of 20 cm. The position and nature of the image formed will be:

a) Between \$-15\$ cm and \$-10\$ cm, virtual and erect

b) At \$-30\$ cm, real, inverted, and diminished

c) At \$-40\$ cm, real, inverted, and same size

d) At \$+15\$ cm, virtual and erect

401 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

401. In which type of mirror does the focal plane lie behind the mirror surface?

a) Concave mirror only.

b) Both concave and convex mirrors.

c) Convex mirror only.

d) None of the above.

402 / 560

Category: Numerical Problems

402. (A) For a concave mirror of focal length 20 cm, if an object is placed at 15 cm from the mirror, the image formed will be virtual and magnified.
(R) For a concave mirror, when the object is placed between the focus and the pole, the image formed is always virtual, erect, and magnified.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

403 / 560

Category: Coordinate Geometry Sign Convention for Measuring Distances and Lengths

403. (A) For a convex mirror, the image formed is always virtual and erect.
(R) The focal length of a convex mirror is positive as per the New Cartesian Sign Convention.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

404 / 560

Category: few Definitions Regarding Spherical Mirrors

404. (A) The principal focus of a concave mirror lies in front of the mirror.
(R) For concave mirrors, the focus is real and lies in front of the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

405 / 560

Category: Definition of Reflection

405. According to the laws of reflection, what is the relationship between the angle of incidence ($i$) and the angle of reflection ($r$)?

a) $i > r$

b) $i < r$

c) $i = r$

d) $i \neq r$

406 / 560

Category: Uses of Spherical Mirrors

406. Why are parabolic mirrors used in searchlights instead of spherical mirrors?

a) They are cheaper to manufacture

b) They produce a perfectly parallel beam without spherical aberration

c) They can be made larger than spherical mirrors

d) They work better in rainy conditions

407 / 560

Category: Convex Mirror (Reflecting surface is outward)

407. A convex mirror has a radius of curvature of 30 cm. If an object is placed 20 cm in front of the mirror, what is the position of the image formed?

a) 5.45 cm

b) 8.57 cm

c) 12.00 cm

d) 15.00 cm

408 / 560

Category: Types of reflection: Regular and Diffuse

408. Why do road signs use retroreflective materials instead of ordinary mirrors, despite both reflecting light?

a) Ordinary mirrors absorb most incident light while retroreflectors absorb none

b) Retroreflectors direct light back toward the source, unlike ordinary mirrors which follow the law of reflection

c) Ordinary mirrors produce regular reflection, making them unsuitable for multi-directional visibility

d) Retroreflectors use diffuse reflection but mirrors use specular reflection

409 / 560

Category: Ray through center → retraces path.

409. A ray of light is directed towards the center of curvature $C$ of a convex mirror. What happens to the ray after reflection?

a) Retrace its original path

b) Become parallel to the principal axis

c) Diverges away from the principal axis

d) Converges at the focus

410 / 560

Category: Velocity of Image

410. An object is moving towards a concave mirror of focal length 20 cm with a speed of 5 cm/s. At a certain instant, the object distance is 30 cm. What is the speed of the image at that instant?

a) 10 cm/s towards the mirror

b) 20 cm/s away from the mirror

c) 15 cm/s away from the mirror

d) 5 cm/s towards the mirror

411 / 560

Category: Concave Mirror:

411. A concave mirror forms a real image when the object is placed:

a) Between F and P

b) Beyond C

c) At F

d) At infinity

412 / 560

Category: Virtual erect image same size → Plane

412. A real object is placed in front of a mirror, and the image formed is virtual, erect, and of the same size as the object. What type of mirror is this?

a) Plane mirror

b) Concave mirror

c) Convex mirror

d) Spherical mirror

413 / 560

Category: Numerical Problems

413. (A) If a concave mirror has a focal length of $-10$ cm, an object placed at $u = -15$ cm will form a real and inverted image.
(R) For a concave mirror, when the object is placed between the focus and the center of curvature, the image formed is real, inverted, and magnified.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

414 / 560

Category: Real image: negative magnification.

414. An object is placed 20 cm in front of a concave mirror of focal length 10 cm. What is the magnification of the image formed?

a) 2

b) -2

c) 1

d) -1

415 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

415. A convex mirror has a radius of curvature of 20 cm. An off-axis parallel ray is incident on the mirror 4 cm away from the principal axis. After reflection, where does the apparent divergence of this ray occur relative to the focal plane?

a) At the virtual focus $F$

b) 4 cm away from $F$ along the principal axis

c) 4 cm away from $F$ perpendicular to the principal axis in the focal plane

d) 8 cm away from $F$ perpendicular to the principal axis in the focal plane

416 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

416. For a spherical mirror with a small aperture, what is the relationship between the focal length ($f$) and the radius of curvature ($R$)?

a) $f = 2R$

b) $f = \sqrt{R}$

c) $f = \frac{R}{2}$

d) $f = R^2$

417 / 560

Category: Virtual erect image same size → Plane

417. A mirror forms a virtual, erect, and same-sized image of an object placed in front of it. What type of mirror is this?

a) Concave mirror

b) Convex mirror

c) Plane mirror

d) Spherical mirror

418 / 560

Category: Virtual erect image same size → Plane

418. (A) A plane mirror forms a virtual, erect image of the same size as the object.
(R) The magnification produced by a plane mirror is +1.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

419 / 560

Category: Laws of reflection

419. According to the laws of reflection, what is the relationship between the angle of incidence and the angle of reflection?

a) The angle of incidence is greater than the angle of reflection

b) The angle of incidence is less than the angle of reflection

c) The angle of incidence is equal to the angle of reflection

d) There is no fixed relationship between the two angles

420 / 560

Category: few Definitions Regarding Spherical Mirrors

420. An object is placed 20 cm in front of a convex mirror with a focal length of 10 cm. Where is the image formed?

a) 20 cm behind the mirror

b) 6.67 cm behind the mirror

c) 10 cm in front of the mirror

d) 5 cm in front of the mirror

421 / 560

Category: Convex Mirror

421. An object is placed at infinity in front of a convex mirror. Where will the image be formed?

a) At the pole of the mirror

b) Between the pole and focus

c) At the focus

d) Beyond the center of curvature

422 / 560

Category: Ray through focus → becomes parallel to axis.

422. A ray of light is directed towards the focus of a convex mirror. After reflection, where does the ray appear to come from?

a) It appears to come from the center of curvature.

b) It appears to come from the pole of the mirror.

c) It appears to come from infinity (parallel to the principal axis).

d) It appears to come from the same point as the object.

423 / 560

Category: Derived for both Concave and Convex mirrors

423. For a concave mirror, if the distance of an object from the focus is 10 cm and the distance of its real image from the focus is 40 cm, what is the focal length of the mirror?

a) 5 cm

b) 10 cm

c) 20 cm

d) 40 cm

424 / 560

Category: Paraxial Rays vs. Marginal Rays

424. What is the focal length ($f$) of a concave mirror for paraxial rays if its radius of curvature ($R$) is 20 cm?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

425 / 560

Category: Mirror Formula

425. (A) For a concave mirror, if the object is placed at a distance of $2f$ from the pole, the magnification produced will be $-1$.
(R) The magnification formula for a spherical mirror is given by $m = -\frac{v}{u}$, and when the object is placed at $2f$, the image is formed at $2f$ on the opposite side with the same size but inverted.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

426 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

426. (A) When an object is placed between the center of curvature $C$ and the principal focus $F$ of a concave mirror, the image formed is real, inverted, and enlarged.
(R) For a concave mirror, when the object distance $u$ satisfies $f < u 1$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

427 / 560

Category: Rear-view mirrors in vehicles

427. Which property of convex mirrors makes them suitable for reducing glare from headlights during nighttime driving?

a) They always form real images

b) They invert the light rays

c) Their diminished images reduce light intensity

d) They require no manual adjustment

428 / 560

Category: Velocity of Image

428. (A) For a concave mirror, if the object moves towards the mirror with velocity $v_o$, the image moves away from the mirror with velocity $v_i = -\left( \frac{v^2}{u^2} \right) v_o$.
(R) The negative sign in the relation between $v_i$ and $v_o$ indicates that the direction of image velocity is opposite to that of the object velocity when the object approaches a concave mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

429 / 560

Category: Convex Mirror

429. (A) The magnification produced by a convex mirror is always less than 1.
(R) A convex mirror always forms a virtual, erect, and diminished image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

430 / 560

Category: Spherical Mirrors

430. An object is placed between the focus and the pole of a concave mirror. What type of image is formed?

a) Real and inverted

b) Virtual and erect

c) Real and erect

d) Virtual and inverted

431 / 560

Category: Sign Conventions (New Cartesian)

431. According to the New Cartesian Sign Convention, which of the following distances is taken as positive?

a) Distance measured to the left of the pole (object side)

b) Distance measured downward below the principal axis

c) Distance measured upward from the principal axis

d) Distance to the focal point of a concave mirror

432 / 560

Category: Searchlights, headlights, solar cookers

432. What is the primary function of a concave mirror in a solar cooker?

a) To disperse sunlight evenly across the cooking pot

b) To absorb sunlight and prevent overheating

c) To reflect and converge sunlight onto the cooking vessel for heating

d) To block harmful ultraviolet rays from reaching the food

433 / 560

Category: Concave: f, R negative; Convex: f, R positive.

433. What is the sign of the focal length (\$f\$) for a concave mirror?

a) Positive

b) Negative

c) Zero

d) Depends on the object distance

434 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

434. An object is placed 10 cm from the pole of a concave mirror with a focal length of 15 cm. The image formed is:

a) Real, inverted, diminished

b) Virtual, erect, diminished

c) Virtual, erect, magnified

d) Real, inverted, magnified

435 / 560

Category: Magnification

435. What is the magnification formula for a spherical mirror?

a) $m = \frac{u}{v}$

b) $m = -\frac{v}{u}$

c) $m = \frac{v}{u}$

d) $m = -\frac{u}{v}$

436 / 560

Category: Ray parallel to axis → passes through focus.

436. If a ray of light parallel to the principal axis strikes a concave mirror, which statement is correct about its reflected path?

a) It reflects perpendicularly away from the mirror's surface

b) It converges at the center of curvature

c) It diverges away from the principal axis

d) It passes through the principal focus

437 / 560

Category: Shaving mirror

437. An ENT doctor uses a concave mirror of focal length 10 cm to examine a patient’s throat. If the doctor wants an image with a magnification of 3, how far should the mirror be held from the patient’s throat?

a) 6.67 cm

b) 7.50 cm

c) 8.33 cm

d) 5.00 cm

438 / 560

Category: Searchlights, headlights, solar cookers

438. In a solar cooker, sunlight (parallel rays) is focused using a concave mirror. If the diameter of the mirror is doubled while keeping its focal length constant, how does the intensity of the focused sunlight change?

a) Intensity becomes half

b) Intensity doubles

c) Intensity remains the same

d) Intensity quadruples

439 / 560

Category: Rear-view mirrors in vehicles

439. Why are convex mirrors preferred over plane mirrors for rear-view purposes in vehicles?

a) They make objects appear larger

b) They provide a narrower but clearer view

c) They give a wider field of view though images are smaller

d) They don't need any adjustment

440 / 560

Category: Spherical Mirrors

440. A concave mirror has a radius of curvature of 40 cm. What is its focal length?

a) 10 cm

b) 20 cm

c) 30 cm

d) 40 cm

441 / 560

Category: Concave Mirror:

441. A concave mirror forms an image twice the size of the object. If the object is placed 15 cm from the mirror, what is the focal length of the mirror?

a) -10 cm

b) -15 cm

c) -30 cm

d) -45 cm

442 / 560

Category: Convex Mirror

442. A convex mirror produces an image with magnification +0.5. What does this indicate about the nature of the image?

a) Real and inverted

b) Virtual and enlarged

c) Virtual and inverted

d) Virtual and diminished

443 / 560

Category: Velocity of Image

443. A concave mirror with focal length $f = 20\text{ cm}$ forms a real image at $v = 60\text{ cm}$. If the object moves towards the mirror at speed $V_{om} = 5\text{ cm/s}$, what is the speed of the image relative to the mirror?

a) 15 cm/s towards the mirror

b) 20 cm/s away from the mirror

c) 10 cm/s towards the mirror

d) 25 cm/s away from the mirror

444 / 560

Category: Real image: negative magnification.

444. (A) For a concave mirror, if the magnification of the image is negative, the image must be real and inverted.
(R) The magnification formula for mirrors is given by $m = -\frac{v}{u}$, where a negative value of $v$ indicates the image is formed on the same side as the object for a concave mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

445 / 560

Category: few Definitions Regarding Spherical Mirrors

445. Which point represents the center of the sphere of which a spherical mirror is a part?

a) Principal axis

b) Centre of curvature

c) Focal point

d) Pole

446 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

446. For a concave mirror, if an object is located at infinity, where does the image form and what are its characteristics?

a) At C, real and inverted

b) At F, real, inverted, and highly diminished

c) Between C and F, virtual and erect

d) Beyond C, real and magnified

447 / 560

Category: Principal Axis – Line joining P and C.

447. A light ray parallel to the principal axis is incident on a concave mirror. After reflection, where will this ray pass through?

a) Option 1: Through the center of curvature (C)

b) Option 2: Through the pole (P)

c) Option 3: Through the focus (F)

d) Option 4: It does not pass through any specific point

448 / 560

Category: Types of reflection: Regular and Diffuse

448. What surface property primarily determines whether reflection will be regular or diffuse?

a) Color of the surface

b) Temperature of the surface

c) Chemical composition

d) Smoothness of the surface

449 / 560

Category: Image Formation by Spherical Mirrors

449. A convex mirror with a focal length of 10 cm forms an image that is one-third the size of the object. What is the object distance?

a) 20 cm

b) 30 cm

c) 40 cm

d) 10 cm

450 / 560

Category: Mirror Formula

450. (A) The mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ is valid for both concave and convex mirrors.
(R) The sign conventions ensure the mirror formula remains applicable for all types of spherical mirrors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

451 / 560

Category: Identification of Mirrors

451. Match the corresponding entries of column-1 with column-2 (where m is the magnification produced by the mirror).

Column-1

(A) $m = -2$

(B) $m = -\frac{1}{2}$

(C) $m = +2$

(D) $m = +\frac{1}{2}$

Column-2

(p) Convex mirror

(q) Concave mirror

(r) Real image

(s) Virtual image

a) A—q and r; B—q and r; C—q and s; D—p and s

b) A—p and r; B—p and s; C—p and q; D—r and s

c) A—p and s; B—q and r; C—q and s; D—q and r

d) A—r and s; B—q and s; C—q and r; D—p and s

452 / 560

Category: Velocity of Image

452. An object moves towards a concave mirror with a velocity of 6 cm/s. At a certain instant, the magnification is $-3$. What is the direction and magnitude of the image velocity?

a) 18 cm/s towards the mirror

b) 54 cm/s away from the mirror

c) 36 cm/s away from the mirror

d) 9 cm/s towards the mirror

453 / 560

Category: few Definitions Regarding Spherical Mirrors

453. What is the definition of the pole of a spherical mirror?

a) The point where light rays converge after reflection

b) The central point of the reflecting surface of the mirror

c) The center of curvature of the mirror

d) The point where the focal length is measured from

454 / 560

Category: Sign Conventions (New Cartesian)

454. A convex mirror forms an image that is one-third the size of the object. If the object distance is 15 cm, what is the magnification and nature of the image?

a) $-\frac{1}{3}$, inverted

b) $\frac{1}{3}$, erect

c) $-3$, inverted

d) $3$, erect

455 / 560

Category: Street lamps for wide area illumination

455. An object is placed 30 cm in front of a concave mirror with a focal length of 20 cm. What is the magnification of the image produced?

a) 1

b) -1

c) 2

d) -2

456 / 560

Category: Mirror Formula

456. According to the sign convention for mirrors, what is the correct sign for the focal length of a convex mirror?

a) Negative

b) Positive

c) Zero

d) Depends on the object distance

457 / 560

Category: Street lamps for wide area illumination

457. If the radius of curvature ($R$) of a convex mirror used in a street lamp is 4 meters, what is its focal length ($f$)?

a) 1 meter

b) 2 meters

c) 4 meters

d) 8 meters

458 / 560

Category: Searchlights, headlights, solar cookers

458. Why are parabolic mirrors preferred over concave spherical mirrors in searchlights?

a) Spherical mirrors are cheaper and easier to manufacture

b) Parabolic mirrors eliminate spherical aberration and produce a perfectly parallel beam

c) Concave mirrors reflect more light than parabolic mirrors

d) Parabolic mirrors have a larger focal length

459 / 560

Category: Between F & P → Behind mirror, virtual, erect, magnified.

459. A concave mirror forms an image that is virtual, erect, and magnified. Where must the object be placed?

a) Beyond the center of curvature

b) At the focus

c) Between focus and pole

d) At infinity

460 / 560

Category: Ray parallel to axis → passes through focus.

460. A ray of light parallel to the principal axis is incident on a concave mirror. After reflection, where will it pass through?

a) The center of curvature

b) The pole of the mirror

c) The focus

d) The same path as the incident ray

461 / 560

Category: For real image: m is negative.

461. (A) For a concave mirror forming a real image, the magnification ($m$) is negative.
(R) A real image formed by a concave mirror is inverted, and the magnification formula accounts for this inversion.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

462 / 560

Category: Reflecting telescopes

462. A reflecting telescope has a primary mirror with a radius of curvature of 200 cm. What is its focal length?

a) 50 cm

b) 100 cm

c) 150 cm

d) 200 cm

463 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

463. For a spherical mirror, if the focal length is 15 cm, what will be its radius of curvature?

a) 7.5 cm

b) 15 cm

c) 30 cm

d) 45 cm

464 / 560

Category: Rules for Image Formation

464. An object is placed at a distance of 30 cm from a concave mirror with a focal length of 20 cm. What is the nature and position of the image formed?

a) Real, inverted, and located 60 cm from the mirror on the object side

b) Virtual, erect, and located 60 cm from the mirror on the opposite side

c) Real, erect, and located 30 cm from the mirror on the object side

d) Virtual, inverted, and located 30 cm from the mirror on the opposite side

465 / 560

Category: Ray obeys law of reflection at surface.

465. What happens when a ray of light is incident normally on a spherical mirror?

a) It reflects perpendicular to the incident ray.

b) It reflects back along the same path.

c) It reflects parallel to the principal axis.

d) It does not reflect at all.

466 / 560

Category: Ray through focus → becomes parallel to axis.

466. Which of the following statements is true about the behavior of a ray incident on a concave mirror after passing through its focus?

a) It diverges away from the principal axis

b) It converges at the pole

c) It travels parallel to the principal axis \ It retraces its original path

467 / 560

Category: Virtual image: positive magnification.

467. Which of the following statements is true regarding the image formed by a convex mirror?

a) A convex mirror can form real images under certain conditions

b) The magnification produced by a convex mirror is always negative

c) The image formed by a convex mirror is always virtual, erect, and diminished

d) A convex mirror gives a magnification greater than 1 when the object is placed beyond its focus

468 / 560

Category: Radius of Curvature (R) – Distance PC.

468. Under what condition is the relation $f = \frac{R}{2}$ strictly valid for spherical mirrors?

a) For all types of rays

b) Only for paraxial rays

c) For large-aperture mirrors

d) Only for diverging rays

469 / 560

Category: Ray through center → retraces path.

469. (A) A ray incident along the principal axis towards the center of curvature of a concave mirror will retrace its path after reflection.
(R) The angle of incidence is zero when a ray is directed towards the center of curvature, resulting in zero angle of reflection.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

470 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

470. Which of the following is true about the focal length ($f$) of a convex mirror?

a) It is negative because the focus is real.

b) It is positive because the focus is virtual.

c) It is zero for all convex mirrors.

d) It depends on the object distance.

471 / 560

Category: Rear-view mirrors in vehicles

471. How does a convex rear-view mirror compare to a plane mirror of the same size when observing traffic behind a vehicle?

a) Both mirrors produce images of the same size and field of view

b) Convex mirror produces larger images but narrower field of view

c) Convex mirror provides a wider field of view but smaller images

d) Plane mirror provides a wider field of view but smaller images

472 / 560

Category: Virtual erect image same size → Plane

472. For which of the following mirrors is the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ applicable?

a) Only concave mirrors

b) Only convex mirrors

c) Both concave and convex mirrors

d) Neither concave nor convex mirrors

473 / 560

Category: Principal Axis – Line joining P and C.

473. A convex mirror forms an image that appears to be located at a distance of $12 \, \text{cm}$ behind the mirror when an object is placed $24 \, \text{cm}$ in front of it. What is the radius of curvature of this convex mirror?

a) 12 cm

b) 24 cm

c) 36 cm

d) 48 cm

474 / 560

Category: Rear-view mirrors in vehicles

474. What type of image is formed by a convex rear-view mirror in vehicles?

a) Virtual, inverted, and magnified

b) Real, erect, and diminished

c) Virtual, erect, and diminished

d) Real, inverted, and magnified

475 / 560

Category: Relation Between Focal Length and Radius of Curvature

475. Two mirrors - one concave (R$_1$ = 40 cm) and one convex (R$_2$ = 60 cm) - are placed coaxially with their reflecting surfaces facing each other. What is the ratio of their focal lengths?

a) 1:1

b) 2:3

c) 3:2

d) 4:9

476 / 560

Category: Street lamps for wide area illumination

476. What happens to the field of view when a convex mirror is used compared to a plane mirror of the same aperture?

a) Field of view decreases

b) Field of view remains the same

c) Field of view increases

d) Field of view becomes zero

477 / 560

Category: Radius of Curvature (R) – Distance PC.

477. What is the correct sign for the focal length of a convex mirror with a radius of curvature of 25 cm?

a) Negative

b) Zero

c) Positive

d) Cannot be determined

478 / 560

Category: Uses of Spherical Mirrors

478. (A) Concave mirrors are used in torches to produce a parallel beam of light.
(R) A concave mirror converges the light from a source placed at its focus into a parallel beam.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

479 / 560

Category: Ophthalmoscopes, ENT examinations

479. If the radius of curvature ($R$) of a concave mirror is 20 cm, what is its focal length ($f$)?

a) 5 cm

b) 10 cm

c) 20 cm

d) 40 cm

480 / 560

Category: Spherical Mirrors

480. Which type of spherical mirror has a reflecting surface curved inwards towards the center of the sphere?

a) Plane mirror

b) Concave mirror

c) Convex mirror

d) Biconvex lens

481 / 560

Category: Focal Plane – Plane through F, perpendicular to principal axis.

481. For a concave mirror, where does a light ray parallel to the principal axis converge after reflection?

a) At the center of curvature.

b) At the principal focus.

c) At the pole of the mirror.

d) It diverges away from the mirror.

482 / 560

Category: Ray obeys law of reflection at surface.

482. An object is placed 40 cm in front of a concave mirror with a radius of curvature of 20 cm. A ray from the object makes an angle of 45 degrees with the principal axis and strikes the mirror. Where does the reflected ray intersect the principal axis?

a) At the focus

b) At the center of curvature

c) $\frac{40}{3}$ cm from the mirror

d) $-\frac{40}{3}$ cm from the mirror

483 / 560

Category: Ray through center → retraces path.

483. A light ray is directed towards the center of curvature of a convex mirror with a radius of curvature 30 cm. What will be the behavior of the reflected ray?

a) The ray reflects parallel to the principal axis

b) The ray diverges away from the center of curvature

c) The ray retraces its path back along the same line

d) The ray converges towards the pole of the mirror

484 / 560

Category: Convex Mirror

484. A convex mirror has a radius of curvature of 40 cm. An object placed at a certain distance produces an image 10 cm behind the mirror. What is the object distance?

a) 10 cm

b) 15 cm

c) 20 cm

d) 25 cm

485 / 560

Category: Virtual image: positive magnification.

485. A convex mirror with focal length 20 cm forms an image of an object placed 60 cm from it. What is the magnification produced?

a) 0.25

b) 0.33

c) 0.50

d) 0.67

486 / 560

Category: Relation Between Focal Length and Radius of Curvature

486. If the radius of curvature of a convex mirror is 20 cm, what is its focal length?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

487 / 560

Category: Image Formation by Spherical Mirrors

487. For a concave mirror with focal length \$-20\, \text{cm}\$, if an object is placed at \$-30\, \text{cm}\$ from the mirror, what is the image distance?

a) $60\, \text{cm}$

b) $-60\, \text{cm}$

c) $40\, \text{cm}$

d) $-40\, \text{cm}$

488 / 560

Category: Concave Mirror:

488. (A) The focal length of a concave mirror is always half its radius of curvature.
(R) The focal point is the midpoint between the pole and the center of curvature of the mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

489 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

489. An object is placed at a distance of 30 cm from a concave mirror with radius of curvature 20 cm. Where will the image be formed and what will be its nature?

a) At 15 cm, virtual and erect

b) At 7.5 cm, real and inverted

c) At 12 cm, virtual and inverted

d) At 20 cm, real and erect

490 / 560

Category: Mirror Formula

490. For a concave mirror, if the distance of the object from the focus is 5 cm and the distance of its real image from the focus is 20 cm, what is the focal length of the mirror?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

491 / 560

Category: Paraxial Rays vs. Marginal Rays

491. If a paraxial ray is incident on a concave mirror of radius of curvature $R = 30$ cm, what is its focal length?

a) 7.5 cm

b) 15 cm

c) 30 cm

d) 60 cm

492 / 560

Category: Shaving mirror

492. Why is a concave mirror preferred over a plane mirror for shaving?

a) It produces an image smaller than the object.

b) It provides a magnified and erect image when the face is within its focal length.

c) It forms a real and inverted image.

d) It reduces glare while shaving.

493 / 560

Category: Ray through center → retraces path.

493. (A) A light ray passing through the center of curvature of a concave mirror retraces its path after reflection.

(R) The angle of incidence and angle of reflection are both zero degrees when the ray passes through the center of curvature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

494 / 560

Category: Pole = origin, principal axis = X-axis.

494. What is the relationship between the focal length ($f$) and the radius of curvature ($R$) for a spherical mirror?

495 / 560

Category: Concave Mirror (Reflecting surface is inward)

495. A concave mirror has a focal length of $-15$ cm. If an object is placed 30 cm from the mirror, where will the image be formed?

a) 10 cm from the mirror, virtual

b) 30 cm from the mirror, real

c) 20 cm from the mirror, real

d) 15 cm from the mirror, virtual

496 / 560

Category: Uses of Spherical Mirrors

496. (A) A concave mirror is used in searchlights to produce an intense parallel beam of light.
(R) A parabolic mirror reflects all rays from its focus as a perfectly parallel beam, unlike a spherical concave mirror which only reflects paraxial rays as parallel.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

497 / 560

Category: Virtual erect image same size → Plane

497. A student observes a virtual, erect, and same-sized image of a candle when placed in front of a mirror. Which of the following statements is correct about the mirror?

a) The mirror has a positive focal length.

b) The mirror forms only real images.

c) The mirror could be either concave or convex.

d) The mirror is flat and does not converge or diverge light.

498 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

498. What is the definition of the focal length ($f$) of a spherical mirror?

a) Distance from the center of curvature to the pole

b) Distance from the pole to the principal focus

c) Half of the radius of curvature

d) Distance from the object to the image

499 / 560

Category: Concave: f, R negative; Convex: f, R positive.

499. (A) In a concave mirror, the focal length (\$f\$) is negative.
(R) The radius of curvature (\$R\$) for a concave mirror is negative according to the sign convention.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

500 / 560

Category: Concave Mirror (Reflecting surface is inward)

500. A concave mirror forms an image that is three times the size of the object. If the object is placed 20 cm from the mirror, what is the focal length of the mirror?

a) -10 cm

b) -15 cm

c) -20 cm

d) -30 cm

501 / 560

Category: Rear-view mirrors in vehicles

501. For a convex rear-view mirror, if an object is placed 5 m away from the mirror with a focal length of 1 m, where will the image be formed?

a) 0.625 m behind the mirror

b) 0.833 m behind the mirror

c) 1.25 m in front of the mirror

d) 2.5 m in front of the mirror

502 / 560

Category: Rear-view mirrors in vehicles

502. (A) In a vehicle's rear-view mirror, the image of an approaching car appears smaller as it gets closer to the mirror.
(R) Convex mirrors always form diminished images and the mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ shows that as $u$ decreases, $v$ also decreases, making the image appear smaller.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

503 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

503. A convex mirror has a radius of curvature of 60 cm. If an object is placed 30 cm in front of it, where will the virtual image form?

a) 10 cm behind the mirror

b) 15 cm behind the mirror

c) 20 cm behind the mirror

d) At infinity

504 / 560

Category: Ray through center → retraces path.

504. If the radius of curvature $R$ of a concave mirror is 20 cm, what is its focal length ($f$)?

a) 5 cm

b) 10 cm

c) 20 cm

d) 40 cm

505 / 560

Category: Identification of Mirrors

505. A mirror forms a real and inverted image of an object placed in front of it. The mirror is:

a) convex mirror

b) concave mirror

c) plane mirror

d) all of these

506 / 560

Category: Introduction to Reflection

506. An object is placed at a distance of 10 cm from a convex mirror of focal length 20 cm. What is the magnification produced by the mirror?

a) 0.5

b) 0.67

c) 1.0

d) 1.5

507 / 560

Category: Uses of Spherical Mirrors

507. What is the primary use of a concave mirror in solar cookers?

a) To disperse sunlight evenly.

b) To reflect light away from the cooker.

c) To absorb sunlight directly.

d) To concentrate sunlight at a focal point.

508 / 560

Category: Principal Focus (F)

508. The principal focus of a concave mirror is:

a) Virtual and lies behind the mirror.

b) Real and lies behind the mirror.

c) Virtual and lies in front of the mirror.

d) Real and lies in front of the mirror.

509 / 560

Category: Ophthalmoscopes, ENT examinations

509. A doctor adjusts a concave mirror for retinal examination. If the retina lies approximately 2 cm behind the eye's lens, what is the minimum distance between the mirror and the patient's eye for effective illumination, assuming the mirror’s focal length is 5 cm?

a) Less than 2 cm

b) Exactly 5 cm

c) Greater than 5 cm

d) 3 cm to 7 cm

510 / 560

Category: Mirror Formula

510. A convex mirror has a focal length of 20 cm. If an object is placed 40 cm from the mirror, what will be the image distance?

a) -13.33 cm

b) 13.33 cm

c) -15.00 cm

d) 15.00 cm

511 / 560

Category: Laws of reflection

511. A light ray strikes a plane mirror at an angle of $30^\circ$ with the normal. What will be the angle between the incident and reflected rays?

a) $30^\circ$

b) $45^\circ$

c) $60^\circ$

d) $90^\circ$

512 / 560

Category: Virtual image: positive magnification.

512. An object is placed between the pole and focus of a concave mirror. How does its image compare when viewed through a convex mirror of same focal length?

a) Both produce same size images

b) Concave gives larger image than convex

c) Convex gives larger image than concave

d) Both produce real images

513 / 560

Category: Velocity of Image

513. If the magnification ($m$) of a concave mirror is $-2$ and the object moves towards the mirror at $5 \, \text{m/s}$, what is the speed of the image?

a) $10 \, \text{m/s}$

b) $-10 \, \text{m/s}$

c) $20 \, \text{m/s}$

d) $-20 \, \text{m/s}$

514 / 560

Category: Aperture (MM’) – Effective diameter of mirror surface.

514. How is the aperture of a mirror typically represented in diagrams?

a) As a curved line along the mirror's surface

b) As a dotted line around the mirror's edge

c) By the line segment $M_1M_2$

d) By an arrow pointing to the mirror's center

515 / 560

Category: few Definitions Regarding Spherical Mirrors

515. (A) For a concave mirror, if the object is placed at the center of curvature, the image formed is real, inverted, and of the same size as the object.
(R) The magnification produced by a concave mirror when the object is placed at the center of curvature is $-1$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

516 / 560

Category: Pole = origin, principal axis = X-axis.

516. Which axis is considered as the principal axis in the Cartesian coordinate system for spherical mirrors?

a) X-axis

b) Y-axis

c) Z-axis

d) Any arbitrary axis

517 / 560

Category: few Definitions Regarding Spherical Mirrors

517. If the radius of curvature $R$ of a concave mirror is 30 cm, what is its focal length $f$?

a) 7.5 cm

b) -7.5 cm

c) 15 cm

d) -15 cm

518 / 560

Category: Mirror Formula

518. What is the mirror formula relating object distance ($u$), image distance ($v$), and focal length ($f$) of a spherical mirror?

a) $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

b) $\frac{1}{v} \times \frac{1}{u} = \frac{1}{f}$

c) $\frac{v}{u} = f$

d) $v + u = f$

519 / 560

Category: Concave Mirror:

519. (A) A concave mirror forms a real image when the object is placed beyond its focal point.
(R) The reflected rays converge to a point on the same side of the mirror as the object, forming an inverted image.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

520 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

520. An object is placed exactly at the center of curvature of a concave mirror. What will be the nature of the image formed when the aperture becomes large enough that marginal rays become significant?

a) Virtual, erect and magnified

b) Real, inverted and diminished

c) Real, blurred image between C and F

d) No image is formed

521 / 560

Category: Searchlights, headlights, solar cookers

521. What type of mirror is used in searchlights to produce an intense parallel beam of light?

a) Plane mirror

b) Convex mirror

c) Parabolic mirror

d) Concave spherical mirror

522 / 560

Category: Ophthalmoscopes, ENT examinations

522. During an ENT examination, a concave mirror produces an erect and enlarged image of the patient's nasal cavity. If the magnification is 2x and the image distance is 20 cm, what is the radius of curvature of the mirror?

a) 10 cm

b) 20 cm

c) 30 cm

d) 40 cm

523 / 560

Category: Types of reflection: Regular and Diffuse

523. A beam of parallel light rays falls on a smooth polished surface and a rough unpolished surface. How does the nature of reflection differ between these two surfaces?

a) Parallel rays diverge equally on both surfaces

b) Parallel rays converge more on the rough surface compared to the smooth one

c) Parallel rays remain parallel only on the smooth surface but scatter randomly on the rough surface

d) Parallel rays scatter more on the smooth surface but remain parallel on the rough surface

524 / 560

Category: Image Formation by Spherical Mirrors

524. An object is placed at a distance of 20 cm from a concave mirror with a focal length of 15 cm. Where will the image be formed?

a) 30 cm in front of the mirror

b) 60 cm behind the mirror

c) 60 cm in front of the mirror

d) 30 cm behind the mirror

525 / 560

Category: Radius of Curvature (R) – Distance PC.

525. If the distance from the pole to the center of curvature of a concave mirror is 50 cm, what is the correct expression for the focal length?

a) $f = 25$ cm

b) $f = -25$ cm

c) $f = 50$ cm

d) $f = -50$ cm

526 / 560

Category: Ophthalmoscopes, ENT examinations

526. Why is a concave mirror used in ENT examinations?

a) To generate heat for sterilization

b) To reflect a convergent beam of light for illumination

c) To absorb excess moisture

d) To block external sounds

527 / 560

Category: Ray through focus → becomes parallel to axis.

527. A ray of light is directed towards the focus of a convex mirror. After reflection, the ray will:

a) Become perpendicular to the principal axis

b) Pass through the center of curvature

c) Become parallel to the principal axis

d) Retrace its path back to the source

528 / 560

Category: Shaving mirror

528. A concave mirror is preferred over a plane mirror for shaving because:

a) It produces a real and inverted image

b) It forms a virtual and diminished image

c) It provides an erect and magnified virtual image

d) It reduces glare and reflections

529 / 560

Category: Convex Mirror

529. (A) A convex mirror always forms a diminished image.
(R) The focal length of a convex mirror is half its radius of curvature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

530 / 560

Category: Centre of Curvature (C) – Center of the sphere of which mirror is part.

530. A convex mirror has radius of curvature 40 cm. An object is placed 60 cm from the pole. What is the magnification produced if the mirror's aperture is very large compared to its radius?

a) 0.15

b) 0.25

c) 0.35

d) 0.45

531 / 560

Category: For real image: m is negative.

531. (A) For a concave mirror, if the magnification $m$ is negative, the image formed is real.
(R) The negative sign in magnification indicates that the image is inverted relative to the object.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

532 / 560

Category: Beyond C → Between C & F, real, inverted, diminished.

532. A concave mirror forms an image at a distance of 15 cm when an object is placed 45 cm in front of it. What can you infer about the nature and position of the image?

a) Virtual, erect, and behind the mirror

b) Real, inverted, and diminished, between C and F

c) Real, inverted, and enlarged, beyond C

d) Virtual, erect, and diminished

533 / 560

Category: Magnification

533. An object is placed 20 cm from a concave mirror of focal length 10 cm. What is the magnification produced?

a) -2

b) -1

c) 1

d) 2

534 / 560

Category: For real image: m is negative.

534. A concave mirror forms a real image of an object placed at a distance of 20 cm from it. If the magnification is $-2$, what is the focal length of the mirror?

a) $-10$ cm

b) $-\frac{40}{3}$ cm

c) $-15$ cm

d) $-20$ cm

535 / 560

Category: Ray obeys law of reflection at surface.

535. A ray of light is incident on a concave mirror at an angle of 30 degrees to the normal. After reflection, it passes through the focal point of the mirror. What is the radius of curvature of the mirror if the distance between the point of incidence and the focal point is 10 cm?

a) 20 cm

b) $10\sqrt{3}$ cm

c) $15$ cm

d) $5\sqrt{2}$ cm

536 / 560

Category: Street lamps for wide area illumination

536. A convex mirror is used in street lamps to illuminate a wide area. What property of the convex mirror allows it to spread light over a larger area?

a) Plane mirror reflects light without divergence

b) Concave mirror converges light to a focal point

c) Convex mirror diverges light rays

d) Flat lens refracts light uniformly

537 / 560

Category: Shaving mirror

537. A person uses a concave shaving mirror with a focal length of 20 cm to get a magnified image of his face. If the image distance is 60 cm, where must the face be placed relative to the mirror?

a) 30 cm from the mirror

b) 40 cm from the mirror

c) 20 cm from the mirror

d) 15 cm from the mirror

538 / 560

Category: Virtual erect image same size → Plane

538. If an object is placed 15 cm in front of a plane mirror, where will the image be formed?

a) 7.5 cm behind the mirror

b) 15 cm in front of the mirror

c) 30 cm behind the mirror

d) 15 cm behind the mirror

539 / 560

Category: Derived for both Concave and Convex mirrors

539. A concave mirror forms an inverted image that is half the size of the object when the object is placed beyond center of curvature. If the object is now moved 15 cm towards the mirror and the new image becomes three times the original object size, what was the initial object distance?

a) 24 cm

b) 27 cm

c) 30 cm

d) 36 cm

540 / 560

Category: Part of a hollow sphere with a polished and reflecting surface.

540. In which of the following cases will a concave mirror produce an image that is larger than the object and inverted?

a) Object placed beyond center of curvature

b) Object placed between focus and pole

c) Object placed at focus

d) Object placed between focus and center of curvature

541 / 560

Category: Ray obeys law of reflection at surface.

541. (A) A light ray incident on a convex mirror surface obeys the laws of reflection.
(R) The angle of incidence is always equal to the angle of reflection for any spherical mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

542 / 560

Category: Concave Mirror:

542. If the magnification (\$m\$) for a concave mirror is negative, what does it imply about the image?

a) The image is virtual

b) The image is highly enlarged

c) The image is inverted

d) The image is diminished

543 / 560

Category: Ophthalmoscopes, ENT examinations

543. What is the primary purpose of using a concave mirror in an ophthalmoscope?

a) To diffract light away from the retina

b) To diverge light and reduce eye strain

c) To reflect and converge light onto the retina

d) To polarize light for better imaging

544 / 560

Category: Rear-view mirrors in vehicles

544. What is the main advantage of using convex mirrors as rear-view mirrors in vehicles?

a) They produce magnified images

b) They provide a wider field of view

c) They form real images

d) They can be used as shaving mirrors

545 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

545. If the angle of incidence $\theta$ is not negligible, what is the general formula for the focal length ($f$) in terms of the radius of curvature ($R$)?

a) $f = \frac{2R}{\cos \theta}$

b) $f = R \cos \theta$

c) $f = \frac{R}{2 \cos \theta}$

d) $f = \frac{\cos \theta}{2R}$

546 / 560

Category: Paraxial Rays vs. Marginal Rays

546. For a spherical mirror with a large aperture, if the angle of incidence ($\theta$) for a marginal ray is $30^\circ$, what is the correct expression for its focal length?

a) $f = \frac{R}{2}$

b) $f = \frac{R}{\cos 30^\circ}$

c) $f = \frac{R}{2 \cos 30^\circ}$

d) $f = \frac{R \cos 30^\circ}{2}$

547 / 560

Category: Ray obeys law of reflection at surface.

547. (A) A ray of light incident at an angle of 30$\degree$ to the normal on a concave mirror with a large aperture will form an image at a different position compared to a paraxial ray due to spherical aberration.
(R) For non-paraxial rays, the focal length is given by $f = \frac{R}{2 \cos \theta}$, where $\theta$ is the angle of incidence, leading to deviation from the standard paraxial behavior.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

548 / 560

Category: Rear-view mirrors in vehicles

548. (A) Convex mirrors are used in vehicles as rear-view mirrors because they provide a wider field of view.
(R) The diminished image formed by convex mirrors helps drivers judge the distance of vehicles behind more effectively.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

549 / 560

Category: Convex Mirror (Reflecting surface is outward)

549. What is the magnification ($m$) for a convex mirror if the object distance ($u$) is $-10$ cm and the image distance ($v$) is $5$ cm?

a) 2

b) 0.5

c) -0.5

d) -2

550 / 560

Category: Paraxial Rays vs. Marginal Rays

550. For a spherical mirror with a small aperture, what is the relation between the focal length ($f$) and the radius of curvature ($R$)?

a) $f = \frac{R}{4}$

b) $f = \frac{R}{2 \cos \theta}$

c) $f = \frac{R}{2}$

d) $f = 2R$

551 / 560

Category: Reflecting telescopes

551. (A) Parabolic mirrors are used in searchlights instead of spherical mirrors.
(R) A parabolic mirror reflects all rays from its focus as a perfectly parallel beam, while a spherical mirror does not.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

552 / 560

Category: Image Formation by Spherical Mirrors

552. (A) A concave mirror always forms a real and inverted image.
(R) A concave mirror converges parallel rays of light to a point called the focus.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

553 / 560

Category: Searchlights, headlights, solar cookers

553. (A) A paraboloidal concave mirror is used in searchlights because it produces a perfectly parallel beam of light when the source is placed at its focus.

(R) The property of a paraboloidal mirror to eliminate spherical aberration ensures that all reflected rays are parallel, unlike a spherical mirror.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

554 / 560

Category: Shaving mirror

554. (A) A concave mirror is preferred over a plane mirror for shaving.
(R) A concave mirror forms a magnified and erect image when the object is placed between its pole and focus.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

555 / 560

Category: Principal Axis – Line joining P and C.

555. What is the relationship between the focal length ($f$) and the radius of curvature ($R$) for a spherical mirror under the paraxial ray approximation?

a) $f = 2R$

b) $f = R$

c) $f = \sqrt{R}$

d) $f = \frac{R}{2}$

556 / 560

Category: Focal Length (f) – Distance PF; f = R/2.

556. A concave mirror with a radius of curvature of 40 cm is used to focus sunlight at its focal point. What will be the approximate diameter of the sun's image on a screen placed at the focal point if the angular diameter of the sun is 0.5°?

a) 0.87 mm

b) 1.745 mm

c) 3.49 mm

d) 0.35 mm

557 / 560

Category: Image Formation by Spherical Mirrors

557. A concave mirror forms a real image at a distance of 40 cm when an object is placed 60 cm from the mirror. What is the focal length of the mirror using Newton's formula?

a) 10 cm

b) 15 cm

c) 20 cm

d) 24 cm

558 / 560

Category: For real image: m is negative.

558. A concave mirror has a focal length of $15$ cm. What should be the object distance to get a magnification of $-3$?

a) $-10$ cm

b) $-15$ cm

c) $-20$ cm

d) $-30$ cm

559 / 560

Category: Between C & F → Beyond C, real, inverted, enlarged.

559. What is the nature of the image formed when an object is placed between \$C\$ and \$F\$ of a concave mirror?

a) Virtual, erect, and diminished

b) Real, inverted, and diminished

c) Virtual, inverted, and enlarged

d) Real, inverted, and enlarged

560 / 560

Category: Concave: f, R negative; Convex: f, R positive.

560. An object is placed 30 cm in front of a convex mirror with a focal length of 15 cm. Calculate the image distance ($v$).

a) $-10$ cm

b) $-7.5$ cm

c) 10 cm

d) 7.5 cm

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Class 12 Physics (Part 2) Chapter 14 Reflection of Light : Spherical Mirrors

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