Chapter 35

The Nature of Light and the Laws of Geometric Optics

Multiple Choice

1. According to Einstein’s theory, the energy of a photon is

a. proportional to its wavelength. b. proportional to its frequency. c. constant, since the speed of light is a constant. d. quantized, since it always appears in bundles of size, 1.6 × 10–19 C. e. proportional to the square of the frequency.

2. Light behaves like

a. a wave at times, and a particle at other times. b. a wave. c. a particle. d. both a wave and a particle, because of its dual nature.

3. The first successful measurement of the speed of light was made by

a. Rene Descartes. b. Armand Fizeau. c. Christian Huygens. d. Ole Roemer. e. James Maxwell.

4. An experiment to measure the speed of light uses an apparatus similar to Fizeau’s. The distance between the light source and the mirror is 10 m, and the wheel has 800 notches. If the wheel rotates at 9000 rev/s when the light from the source is extinguished, what is the experimental value for c (in m/s)?

a. 2.94 × 108 b. 2.92 × 108 c. 2.88 × 108 d. 2.98 × 108 e. 3.01 × 108

5. A light ray is incident on the surface of water (n = 1.33) at an angle of 60° relative to the normal to the surface. The angle of the reflected wave is

a. 80° b. 40° c. 20° d. 60° e. 30°

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250 CHAPTER 35

6. A light ray whose frequency is 6 × 1014 Hz in vacuum is incident on water (n = 1.33). The wavelength of the light after it enters the water is (in nm)

a. 798 b. 500 c. 665 d. 376 e. 266

7. The speed of light changes when it goes from ethyl alcohol (n = 1.361) to carbon tetrachloride (n = 1.461). The ratio of the speed in carbon tetrachloride to the speed in ethyl alcohol, v2/v1, is

a. 1.99 b. 1.07 c. 0.93 d. 0.51 e. 0.76

8. Light is refracted through a diamond. If the angle of incidence is 30°, and the angle of refraction is 12°, what is the index of refraction?

a. 1.3 b. 2.4 c. 2.6 d. 1.8 e. 0.4

9. Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface?

a. 30° b. 60° c. 45° d. 53° e. 75°

10. Two mirrors are at right angles to one another. If an object is placed near the mirrors, what is the largest number of images that would be seen in the mirrors?

a. 3 b. 2 c. 4 d. 5 e. 6

The Nature of Light and the Laws of Geometric Optics 251

11. A person in a boat sees a fish in the water (n = 1.33), the light rays making an angle of 40° relative to the water’s surface. What is the true angle (in degrees) relative to the water’s surface of the same rays when beneath the surface?

a. 40 b. 35 c. 50 d. 55 e. 61

12. A fish is 80 cm below the surface of a pond. What is the apparent depth (in cm) when viewed from a position almost directly above the fish? (For water, n = 1.33.)

a. 50 b. 60 c. 40 d. 70 e. 110

13. A diver shines light up to the surface of a flat glass-bottomed boat at an angle of 30° relative to the normal. If the index of refraction of water and glass are 1.33 and 1.5, respectively, at what angle (in degrees) does the light leave the glass (relative to its normal)?

a. 26 b. 35 c. 42 d. 22 e. 48

14. A person looks horizontally at the edge of a swimming pool. If its length is 5 m, and the pool is filled to the surface, to what depth (in m) could the observer see? (n for water is 1.33)

a. 3.2 b. 4.4 c. 2.1 d. 1.0 e. 0.3

15. An aquarium contains a 5-cm layer of water (n = 1.33) floating on top of carbon tetrachloride (n = 1.461). If the angle of incidence into the water from the air is 30°, what is the angle of refraction into the carbon tetrachloride?

a. 58° b. 69° c. 37° d. 20° e. 75°

252 CHAPTER 35

16. An aquarium contains a 5-cm layer of water (n = 1.333) floating on top of carbon tetrachloride (n = 1.461). If the angle of incidence into the water from the carbon tetrachloride is 20°, what is the angle of refraction into the air?

a. 20° b. 30° c. 38° d. 69° e. 26°

17. Light strikes a diamond (n = 2.42) at an angle of 60° relative to the normal to the surface. What is the angle of refraction?

a. 21° b. 30° c. 38° d. 69° e. 71°

18. Light strikes a diamond (n = 2.42) immersed in glycerin (n = 1.473) at an angle of 60° relative to the normal to the surface. What is the angle of refraction?

a. 20° b. 60° c. 32° d. 64° e. 15°

19. A diver shines an underwater searchlight at the surface of a pond (n = 1.33). At what angle (relative to the surface) will the light be totally reflected?

a. 47° b. 41° c. 51° d. 58° e. 49°

20. A layer of ethyl alcohol (n = 1.361) is on top of water (n = 1.333). At what angle relative to the normal to the interface of the two liquids is light totally reflected?

a. 78° b. 88° c. 68° d. 49° e. the critical angle is undefined

The Nature of Light and the Laws of Geometric Optics 253

21. A layer of water (n = 1.333) floats on carbon tetrachloride (n = 1.461) contained in an aquarium. What is the critical angle at the interface between the two liquids?

a. 88° b. 78° c. 66° d. 58° e. 43°

22. The figure shows a prism with parallel sides made of a material with a variable index of refraction. The index of refraction increases from left to right. The figure also shows a wave front as it reaches the prism. Which of the figures in the answers correctly shows the most probable position of the wave front in the prism just before the light starts to leave the prism?

wavefront

low n high n

(a) (b)� (c)� (d)� (e)

23. A monochromatic (single frequency, single wavelength) light ray in air (n = 1) enters a glass prism (n = 1.5). In the glass prism

a. both the frequency and the wavelength are the same as in air b. the frequency is the same, but the wavelength is greater than in air. c. the frequency is the same, but the wavelength is smaller than in air. d. the wavelength is the same, but the frequency is greater than in air. e. the wavelength is the same, but the frequency is smaller than in air.

254 CHAPTER 35

24. A light ray is partially reflected and partially refracted at a boundary between two media, the upper one having index of refraction n, the lower one having index of refraction n′, as shown in the figure. The reflected ray is perpendicular to the refracted ray when

incident reflected

refracted

n

n′

a. n′ = n tan θincident. b. n′ = n cot θincident.

c. n′ = n reflection

incident

θθ

sinsin

.

d. n′ = n reflection

reflection

θθ

sin

sin.

e. n′ = n sec θincident.

25. A light ray strikes a hexagonal ice crystal floating in the air perpendicular to one face, as shown below. The hexagonal faces of the crystal are perpendicular to the plane of the page. All the rays shown are in the plane of the page, and nice = 1.30. Which outgoing ray is correct when the incoming ray strikes the crystal face on the left head on?

A

B

C

D

E a. A b. B c. C d. D e. E

The Nature of Light and the Laws of Geometric Optics 255

26. A light ray strikes a hexagonal ice crystal floating in the air at a 30° angle to one face, as shown below. The hexagonal faces of the crystal are perpendicular to the plane of the page. All the rays shown are in the plane of the page, and nice = 1.30. Which outgoing ray is the correct one?

A

B

C

D

E a. A b. B c. C d. D e. E

27. When a light ray travels between any two points, the path it takes is the one that

a. covers the greatest distance. b. follows the greatest index of refraction. c. avoids travel in more than one medium. d. is the mean between the longest and the shortest paths. e. takes the least time.

28. The wave front shown at the left for light in air reaches the plane boundary between air and two transparent mediums with n1 = 1.5 and n2 = 3.00 respectively.

n1

n2

Which diagram below correctly illustrates the wave front after it has entered the two mediums at the right?

n1

n2

A�

n1�

n2

B�

n1

n2

C�

n1

n2

D�

n1

n2

E a. A b. B c. C d. D e. E

256 CHAPTER 35

29. The wave front shown at the left for light in air reaches the plane surface (shown by a slanted line) that bounds a medium with n = 1.50.

Which diagram below correctly shows the wave front while entering the medium at the right?

A B C D E a. A b. B c. C d. D e. E

30. Light can exhibit the characteristics of

= hfa. a particle with energy . E

b. a wave with wavelength λ =

hcE

.

c. a particle or wave that travels at speed c = 3.0

ms

0 × 108 in all materials.

d. all of the above. e. only (a) or (b) above.

31. When light scatters from a rough surface, the law ′θ = θ1 1

a. does not hold. b. holds on average, with reflected light from the surface leaving in the

average direction of reflection. c. applies to each small relatively flat area of surface individually. d. applies only when the particle aspect of light predominates. e. applies only when the wavelength of light is greater than 800 nm but less

than 2000 nm.

The Nature of Light and the Laws of Geometric Optics 257

32. Two flat rectangular mirrors are set edge to edge and placed perpendicular to a flat nonreflecting surface. A light ray that reflects from mirror 1 at angle θM1 then

strikes the second mirror and reflects at θM2 such that the angle between the ray reaching mirror 1 and the ray leaving mirror 2 is 180° . The angle between the two mirrors is

a. 0° . b. 45° . c. 90° . d. 180° . e. 235° .

33. The angle between two plane mirrors that meet at one edge is 45° . The change in direction of a ray that strikes the first mirror at a 60° angle of incidence when that ray reflects from the second mirror is

0° . a. 45° . b. 90° . c. 180° . d.

e. 270° .

34. When light is either reflected or refracted, the quantity that does not change in either process is its

a. direction of travel. b. dispersion. c. frequency. d. speed. e. wavelength.

35. Two flat rectangular mirrors are set edge to edge and placed perpendicular to a flat nonreflecting surface. The edges of the two mirrors meet at a 30° angle. A light ray that approaches mirror 1 is parallel to mirror 2. The angle of reflection of that ray from mirror 1 is

0° . a. 30° . b.

c. 60° . d. 90° . e. 120° .

36. Two flat rectangular mirrors are set edge to edge and placed perpendicular to a flat nonreflecting surface. The edges of the two mirrors meet at a 30° angle. A light ray that enters parallel to mirror 2 reflects from mirror 1 and then from mirror 2. The angle of reflection of that ray from mirror 2 is

0° . a. b. 30° . c. 60° . d. 90° . e. 120° .

258 CHAPTER 35

Open-Ended Problems

37. A soda straw is stuck into water at an angle of 36° to the vertical. Looking straight down, what does the angle of the submerged portion of the straw to the vertical appear to be?

38. A laser beam is incident from the air at an angle of 30° to the vertical onto a solution of Karo syrup in water. If the beam is refracted to 19.24° to the vertical, what is the index of refraction of the syrup solution?

39. A layer of kerosene (n = 1.45) is floating on water (n = 1.33). For what angles of incidence at the kerosene-water interface will light be totally internally reflected within the kerosene?

40. The index of refraction for red light in water is 1.331 and for blue light is 1.340. If a ray of white light enters the water at an angle of incidence of 83°, what are the underwater angles of refraction for the blue and red components of the light?

41. The laws of refraction and reflection are the same for sound as for light. The speed of sound in air is 340 m/s and in water it is 1510 m/s. If a sound wave approaches a plane water surface at an angle of incidence of 12°, what is the angle of refraction?

The Nature of Light and the Laws of Geometric Optics 259

Chapter 35

The Nature of Light and the Laws of Geometric Optics

1. b

2. a

3. d

4. c

5. d

6. d

7. c

8. b

9. b

10. a

11. d

12. b

13. c

14. b

15. d

16. b

17. a

18. c

19. b

20. a

21. c

22. d

23. c

24. a

25. c

26. b

27. e

28. c

29. b

30. e

31. c

32. c

33. e

34. c

35. c

36. b

37. 44°

38. 1.517

39. θ > 66.5°

40. 47.79° (blue), 48.22° (red)

41. 67.4°

260 CHAPTER 35