REVIEWING CONCEPTS

1. What is meant by the normal to a surface? 2. How does regular reflection differ from diffuse

reflection? 3. Does the law of reflection hold for diffuse re­

flection? Explain. 4. Copy Figure 1 7 - 1 7 onto your paper. Draw a

normal and label the angle of incidence and the angle of refraction if the light went f rom substance A to substance B.

A B

Substance

FIGURE 17-17. Use with Reviewing Concepts 4 and Applying Concepts 7.

5. Compare the angle of incidence with the angle of refraction when a light ray passes from air into glass at a non-zero angle.

6. Compare the angle of incidence with the angle of refraction when a light ray leaves glass and enters air at a non-zero angle.

7. What are the units of the index of refraction? 8. State Snell's law in your own words.

9. Derive n = sin 6 :

from the general form of sin 6 ,

Snell's law, n, sin = n 2 sin d2. State any assumptions and restrictions.

10. What is the "critical angle" of incidence? 11. What happens to a ray of light with an angle

of incidence greater than the critical angle? 12. Explain mirages. 13. List the different colors of light in the order of

increasing a. wavelength. b. frequency.

14. What evidence is there that diamond has a slightly different index of refraction for each color of light?

APPLYING CONCEPTS

1. A dry road is a diffuse reflector, while a wet road is not. Sketch a car with headlights illu­minating the road ahead. Show why the wet road would appear darker to the driver than the dry road.

2. Why is it desirable that the pages of a book be rough rather than smooth and glossy?

3. Is it necessary to measure the volume of a glass block to find its optical density? Explain.

4. A light ray strikes the boundary between two transparent media. What is the angle of inci­dence for which there is no refraction?

5. In the Example Problem on Snell's law, a ray of light is incident upon crown glass at 3 0 . 0 ° . The angle of refraction is 19.2° . Assume the glass is rectangular in shape. Construct a dia­gram to show the incident ray, the refracted ray, and the normal. Continue the ray through the glass until it reaches the opposite edge. a. Construct a normal at this point. What is

the angle at which the refracted ray is in­cident upon the opposite edge of the glass?

b. Assume the material outside the opposite edge is air. What is the angle at which the ray leaves the glass?

c. As the ray leaves the glass, is it refracted away from or toward the normal?

d. How is the orientation of the ray leaving the glass related to the ray entering the glass?

6. Assume the angle of incidence remains the same. What happens to the angle of refrac­tion as the index of refraction increases?

7 . Which substance, A or B, in Figure 1 7 - 1 7 has a larger index of refraction? Explain.

8. How does the speed of light change as the index of refraction increases?

9. How does the size of the critical angle change as the index of refraction increases?

10. Which two pairs of media, air and water or air and glass, have the smaller critical angle?

11. Examine Figure 1 7 - 5 . Why do the two left-hand bottom rays that enter the prism exit vertically while the two top rays exit horizon­tally? Hint: If you look carefully, you will f ind that the middle ray has both vertical and hor­izontal intensity and that there is a trace of the other ray moving vertically.

12. If you crack the windshield in your car, you will see a silvery line along the crack. The two pieces of glass have separated at the crack, and there is air between them. The silvery line indicates light is reflecting off the crack. Draw a ray diagram to explain why this occurs. What phenomenon does this illustrate?

Chapter 17 Review 3 6 3

EVALUATION MASTER X Use the Chapter Evaluation master for Chapter 17 with this section.

Answers T o REVIEWING CONCEPTS 1. any line that is perpendicular

to the surface at any point 2. When parallel light is reflected

from a smooth surface, the rays are reflected parallel to each other. The result is an image of the origin of the rays. When light is reflected from a rough surface, it is reflected in many different directions. The rays are diffused or scattered. No image of the source results. 3. Yes. Each individual ray fol­

lows the law of reflection. Because the surface is rough, the normals at individual locations are typically not parallel to each other. There­fore, the reflected rays are not par­allel to each other. 4.

5. The angle of incidence is larger than the angle of refraction, since air has a smaller index of re­fraction. 6. The angle of incidence is

smaller than the angle of refrac­tion, since glass has a larger index of refraction. 7. The index of refraction has no

units. 8. Whenever a ray of light passes

from one medium into another at some angle, the ray is refracted in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for all angles of inci­dence. 9. The angle of incidence must

be in air. If we let substance 1 be air, then n, = 1.000, fl-, = 6, and 02 = 0r- Therefore,

= n 2 sin e 2 n-, sin 01 = n 2

sin 8\ = n sin 6 r

sin 6>j sin dr

n

10. The term "critical angle" refers to the incident angle that causes the refracted ray to lie right along the boundary of the substance when a ray is passing from a dense to less dense medium. It may also be termed the incident angle, which, if exceeded, will cause total internal reflection.

Reflection and Refraction 363

• 15. A sheet of plastic, n = 1.500, 25 mm thick is used in a bank teller's window. A ray of light strikes the sheet at an angle of 45°. The ray leaves the sheet at 45° but at a different lo­cation. Use a ray diagram to find the distance between the ray that leaves and the one that would have left if the plastic were not there.

16. What is the speed of light in diamond? 17. The speed of light in chloroform is 1.99 x

10s m/s. What is its index of refraction? • 18. The speed of light in a clear plastic is 1.90 x

10s m/s. A ray of light enters the plastic at an angle of 22°. At what angle is the ray re­fracted?

• 19. How many more minutes would it take light from the sun to reach Earth if the space be­tween them were filled with water rather than a vacuum? The sun is 1.5 x 108 km from Earth.

17.2 Appl icat ions o f Reflected and Refracted Light

20. Find the critical angle for diamond. 21. A block of glass has a critical angle of 45.0°.

What is its index of refraction? 22. A ray of light in a tank of water has an angle

of incidence of 55°. What is the angle of re­fraction in air?

• 23. A light ray enters a rectangle of crown glass, Figure 17 -20 . Use a ray diagram to trace the path of the ray until it leaves the glass.

• 26. The index of refraction for crown glass for red light is 1.514, while that for blue light is 1.528. White light is incident on the glass at 30.0°. a. Find the angles of refraction for these two

colors. b. Compare the difference in angles to that

for diamond found in Problem 25. c. Use the results to explain why diamonds

are said to have "f ire." 27. The index of refraction of crown glass for vi­

olet light is 1.53, while for red light it is 1.51. a. What is the speed of violet light in crown

glass? b. What is the speed of red light in crown

glass? 28. Just before sunset, you see a rainbow in the

water from a lawn sprinkler. Carefully draw your location and the locations of the sun and the water from the sprinkler that show the rainbow.

THINKING PHYSIC-LY

Although the light coming from the sun is re­fracted while passing through Earth's atmo­sphere, the light is not separated into its spec­trum. What does this tell us about the speeds of different colors of light traveling through air?

FIGURE 17-20. Use with Problem 23.

24. The critical angle for special glass in air is 41°. What is the critical angle if the glass is immersed in water?

25. The index of refraction for a diamond for red light, 656 nm, is 2.410, while that for blue light, 434 nm, is 2.450. Suppose white light is incident on the diamond at 30.0°. Find the an­gles of refraction for these two colors.

Chapter 17 Review 365

16. 1.24 x 108 m/s 17. 1.51 18. 14° 19. 2.7 min 20. 24.4° • 21. 1.41 . 22. no angle 23. Refer to Problems and Solu­

tions Manual. 24. 61° 25. red, 12.0°; blue, 11.8° 26. a. red, 19.3°; blue, 19.1°

b. diamond difference: red, 18.0°; blue, 18.2°; crown glass difference: red, 10.7°; blue, 10.9°

c. more red light emerges than blue light

27. a. 1.96 x 108 m/s b. 1.99 x 108 m/s

28. Refer to Problems and Solu­tions Manual.

A n s w e r T o

THINKING PHYSIC-LY The fact that the light is not sepa­rated into its spectrum shows that different colors of light travel through air at almost exactly the same speed.

12.

C r a c k

This illustrates light reflected at ar gles larger than the critical angle. 1 3 .

Even though Greenland is belo the horizon, it is visible as a mirag due to the refraction of light. 14. Violet light travels slower in prism than red light. 15. Red light because it is r< fracted the least by glass. 16. You can see a rainbow on when the sun's rays come from be hind you at an angle not great< than 42° with the horizon. Whe you are facing south in the nortl ern hemisphere, the sun is nevt behind you at an angle of 42° < less.

A n s w e r s T o

PROBLEMS Compete solutions for all Chapte Review Problems can be found i the Problems and Solutions Mar ual accompanying this text. 1. a. 53°

b. 106° 2. 108° 3. 1.46 4. a. 1.34

b. water 5. 34.7° 6. 26.2° 7. 21.0° 8. 55.9° 9. 20.2°

10. 20.9° 11. a. 25°

b. 29° 12. 49.8° *fY r ' 13. a. 53°

b. shallower 14. a. 28°

b. A, 62°; B, 58°; C, 32' c. 53°

15. 8 mm

Reflection and Refraction