Reflection and Refraction of Light

Choose the best answer for each question. All angles of incidence and reflection are measured from the normal unless otherwise stated.

1. Ray P makes an angle of 28° with the surface of a plane mirror. Ray Q has an angle of incidence of 48°. How do their angles of reflection compare?
   1. Ray P’s angle is 14° greater than Ray Q’s.
   2. Ray P’s angle is 20° greater than Ray Q’s.
   3. Ray Q’s angle is 14° greater than Ray P’s.
   4. Their angles of reflection are equal.
2. A fixed incident ray strikes a plane mirror with an angle of incidence of 34°. The mirror is then rotated by 7° so that the angle of incidence increases. Which pair gives the new angle of incidence and the change in direction of the reflected ray?
   1. 41° and 7°
   2. 41° and 14°
   3. 48° and 7°
   4. 48° and 14°
3. An object is initially 3.2 m in front of a stationary plane mirror. It then moves 0.75 m towards the mirror. Which statement correctly describes the final situation?
   1. The image is 2.45 m behind the mirror, and the object–image distance has decreased by 0.75 m.
   2. The image is 2.45 m behind the mirror, and the object–image distance has decreased by 1.50 m.
   3. The image is 3.95 m behind the mirror, and the object–image distance has increased by 1.50 m.
   4. The image is 2.45 m behind the mirror, and the object–image distance is 3.20 m.
4. A stationary object is 1.8 m in front of a plane mirror. The mirror is moved 0.30 m towards the object. Relative to its original position, how far and in which direction does the image move?
   1. 0.30 m towards the object
   2. 0.30 m away from the object
   3. 0.60 m towards the object
   4. 0.60 m away from the object
5. Four students record the angle that an incident ray makes with a mirror surface and the angle that the reflected ray makes with the normal. Which result is consistent with the law of reflection?

   Option	Incident ray with mirror surface	Reflected ray with normal
   A	24°	24°
   B	37°	53°
   C	53°	53°
   D	68°	12°

   1. Result A
   2. Result B
   3. Result C
   4. Result D
6. A plane mirror lies along the position x = 0. An object is at x = −2.3 m, and an observer is at x = −0.7 m. The object then moves to x = −1.5 m, while the observer moves to x = −1.1 m. How does the apparent distance from the observer to the image change?
   1. It decreases from 3.0 m to 2.6 m.
   2. It decreases from 3.0 m to 0.4 m.
   3. It increases from 1.6 m to 2.6 m.
   4. It remains unchanged at 3.0 m.
7. A student says, “A plane-mirror image is virtual because reflected rays actually meet behind the mirror, but the image cannot be formed on a screen.” Which evaluation is correct?
   1. The entire explanation is correct.
   2. The image is real because the reflected rays meet behind the mirror.
   3. The reflected rays do not actually meet behind the mirror; only their backward extensions appear to meet there.
   4. The image is virtual because it is smaller than the object.
8. Object P is 1.4 m in front of a plane mirror, while object Q is 3.8 m in front of the same mirror. Which pair of distances is correct?

   Option	Distance between the two images	Distance from P to the image of Q
   A	2.4 m	2.4 m
   B	2.4 m	5.2 m
   C	5.2 m	2.4 m
   D	5.2 m	5.2 m

   1. Pair A
   2. Pair B
   3. Pair C
   4. Pair D

Choose the best answer for each question. Use c = 3.0 × 10⁸ m/s and n = c/v where necessary. For light travelling from air into a material, use n = sin i / sin r.

1. Light travels at 2.0 × 10⁸ m/s in material P and at 2.4 × 10⁸ m/s in material Q. Which statement is correct?
   1. P has a refractive index of 1.20 and is less optically dense than Q.
   2. P has a refractive index of 1.50 and is more optically dense than Q.
   3. Q has a refractive index of 1.50 and is more optically dense than P.
   4. P and Q have the same optical density because light travels quickly in both.
2. A transparent material has a refractive index of 1.60. What is the speed of light in the material?
   1. 1.60 × 10⁸ m/s
   2. 1.88 × 10⁸ m/s
   3. 2.40 × 10⁸ m/s
   4. 4.80 × 10⁸ m/s
3. Material X has a refractive index of 1.25, while material Y has a refractive index of 1.50. What is the ratio of the speed of light in X to the speed of light in Y?
   1. 0.83
   2. 1.00
   3. 1.20
   4. 1.88
4. Light travels from air into a material. Measurements give sin i = 0.766 and sin r = 0.500. Which pair is the best estimate of the material’s refractive index and the speed of light in the material?

   Option	Refractive index	Speed of light
   A	0.65	4.6 × 108 m/s
   B	1.27	2.4 × 108 m/s
   C	1.53	2.0 × 108 m/s
   D	1.53	4.6 × 108 m/s

   1. Pair A
   2. Pair B
   3. Pair C
   4. Pair D
5. A student measures the refraction of light from air into the same glass block four times. Which result is most likely to be inaccurate?

   Result	sin i	sin r
   A	0.342	0.228
   B	0.500	0.333
   C	0.707	0.471
   D	0.866	0.667

   1. Result A
   2. Result B
   3. Result C
   4. Result D
6. Light enters materials P and Q from air at the same angle of incidence. For both rays, sin i = 0.70. In P, sin r = 0.50, while in Q, sin r = 0.40. Which conclusion is correct?
   1. P has a refractive index of 1.75 and is more optically dense than Q.
   2. Q has a refractive index of 1.75 and light travels more slowly in Q.
   3. Q has a refractive index of 1.40 and light travels faster in Q.
   4. Both materials have the same refractive index because the incident angles are equal.
7. A student plots sin i on the vertical axis and sin r on the horizontal axis for light travelling from air into glass. The graph is a straight line through the origin with a gradient of 1.52. What can be concluded?
   1. The refractive index is 0.66, and light travels at 4.6 × 10⁸ m/s.
   2. The refractive index is 1.52, and light travels at approximately 2.0 × 10⁸ m/s.
   3. The refractive index is 1.52, and light travels at approximately 4.6 × 10⁸ m/s.
   4. The refractive index is 2.0, and light travels at 1.52 × 10⁸ m/s.
8. The speed of light in a material is 20% lower than its speed in a vacuum. What is the refractive index of the material?
   1. 0.80
   2. 1.20
   3. 1.25
   4. 1.80
9. A student claims that a material’s refractive index is i/r. The student measures i = 60° and r = 35°, obtaining a value of 1.71. Which response is correct?
   1. The answer is correct because 60 ÷ 35 = 1.71.
   2. The student should calculate sin 35° / sin 60°, giving approximately 0.66.
   3. The student should calculate sin 60° / sin 35°, giving approximately 1.51.
   4. The student should subtract the angles, giving a refractive index of 25.
10. A ray enters material X from air with sin i = 0.75. Material X has a refractive index of 1.40. A second ray enters material Y at the same angle of incidence. Material Y has a refractive index of 1.70. Which pair gives the approximate values of sin r?

    Option	Material X	Material Y
    A	0.44	0.54
    B	0.54	0.44
    C	0.75	0.75
    D	1.05	1.28

    1. Pair A
    2. Pair B
    3. Pair C
    4. Pair D
11. A ray enters a transparent material from air along the normal. The material has a refractive index of 1.50. Which statement is correct?
    1. The ray bends towards the normal, and its speed becomes 2.0 × 10⁸ m/s.
    2. The ray bends away from the normal, and its speed becomes 2.0 × 10⁸ m/s.
    3. The ray does not bend, but its speed becomes 2.0 × 10⁸ m/s.
    4. The ray does not bend, and its speed remains 3.0 × 10⁸ m/s.
12. A student investigates two transparent materials.

    Material	Refractive index
    P	1.35
    Q	1.62

    Which conclusion is not supported by the information?
    1. Light travels more slowly in Q than in P.
    2. Q is more optically dense than P.
    3. For the same angle of incidence from air, light bends more towards the normal in Q.
    4. Q must have a greater mass density than P.

Write “True” or “False” for each statement. If a statement is false, rewrite it correctly.

1. A ray that makes an angle of 27° with a mirror surface has an angle of reflection of 63°.
2. If an incident ray and a reflected ray make equal angles with the mirror surface, they also make equal angles with the normal.
3. A fixed incident ray strikes a mirror. If the mirror rotates through 4°, the reflected ray changes direction by 8°.
4. When an object moves 0.30 m towards a stationary plane mirror, the distance between the object and its image decreases by 0.60 m.
5. If a plane mirror moves 0.20 m towards a stationary object, its image moves 0.40 m towards the object.
6. The reflected rays from a plane mirror do not actually pass through the position of the image, although they appear to come from that position.
7. If an observer moves towards a stationary plane mirror while the object remains stationary, the position of the object’s image also moves towards the mirror.
8. A plane-mirror image is the same size as its object, but it cannot be projected directly onto a screen.
9. If the angle of incidence increases by 10°, the angle between the incident ray and the mirror surface decreases by 10°.
10. At normal incidence, the reflected ray returns along the path of the incident ray in the opposite direction.
11. If light passes between two media without changing speed, it will not bend at the boundary.
12. A more optically dense material has a higher refractive index and a lower speed of light.
13. If the refractive index of a material is 1.50, light travels through it at 2.0 × 10⁸ m/s.
14. Light travels 1.20 times faster in a material with a refractive index of 1.50 than in a material with a refractive index of 1.25.
15. For light travelling from air into a particular material, the ratio i/r remains constant as the angle of incidence changes.
16. A student finds that sin i / sin r = 1.60. This means that light travels through the material at approximately 1.88 × 10⁸ m/s.
17. Two rays entering the same material at different angles travel at different speeds inside the material.
18. Two rays enter different materials from air with the same angle of incidence. The ray with the smaller angle of refraction enters the material with the higher refractive index.
19. When a ray enters a glass block along the normal, its speed changes even though its direction does not change.
20. A substance that is more optically dense must also have a greater mass density.