•39 In Fig. 34-38, a beam of parallel light rays from a laser is in-cident on a solid transparent sphere of index of refraction n. (a) Ifa point image is produced at theback of the sphere, what is the indexof refraction of the sphere? (b)What index of refraction, if any, willproduce a point image at the centerof the sphere?

Answered: Image /qna-images/answer/ece4012c-7790-42a4-9708-05e3c3650eca.jpg

Answered: •39 In Fig. 34-38, a beam of parallel…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter38: Refraction And Images Formed By Refraction

Section: Chapter Questions

Problem 104PQ

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In Section 9.6, we described how the speed of light varies with wavelength (or frequency) for transparent solids. But the speed of light in matter is also a function of temperature and pressure. This dependence is most marked for gases and is instrumental in producing such things as mirages and atmospheric refraction, the latter phenomenon being the displacement of an astronomical object (like the Sun or another star) from its true position because of the passage of its light through the atmosphere. Because Earth’s atmosphere is a gaseous mixture and easily compressed, its density is highest near Earth’s surface and gradually declines with altitude. (Refer to the discussion in Section 4.4 and Figure 4.29.) Thus, the speed of light in the atmosphere is lowest near the surface and gradually gets higher, approaching c as one goes farther and farther into space. Using this fact and the law of refraction, sketch the path a light ray from the Sun would follow upon entering Earth’s atmosphere, and predict the apparent position of the Sun relative to its true position (Figure 9.85). What does this tell you about the actual location of the Sun’s disk relative to your local horizon when you see it apparently setting brilliantly in the west in the evening?
A ray of 610 nm light goes from air into fused quartz at an incident angle of 55.0°. At what incident angle must 470 nm light enter flint glass to have the same angle of refraction?
Suppose a certain person’s visual acuity is such that he can see objects clearly that form an image 4.00mhigh on his retina. What is the maximum distance at which he can read the 75.0-cm-high letters on the side of an airplane?
•45 When the rectangular metal tank in Fig. 33-46 is filled to the top with an unknown liquid, observer o- O, with eyes level with the top of the tank, can just see corner E. A ray that refracts toward O at the top surface of the liquid is shown. If D = 85.0 cm and L = 1.10 m, what -Normal to liquid surface is the index of refraction of the liquid? -L-
•48 In Fig. 33-48a, a light ray in water is incident at angle 61 on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction 6, versus the incident angle 6, is given in Fig. 33-48b. The vertical axis scale is set by 6, = 90°. %3D Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water (n = 1.33). What is the index of refraction of (c) material 1 and (d) material 2? Ө, в2. Water 0° 45° 90° (a) (6)
•4 In Fig. 35-32a, a beam of light in material 1 is incident on a boundary at an angle of 30°. The extent to which the light is ben due to refraction depends, in part, on the index of refraction n, o material 2. Figure 35-32b gives the angle of refraction Oz versus n for a range of possible n2 values, from n, = 1.30 to n, = 1.90. Wha is the speed of light in material 1? в, 40° 300! 30° в, 20° по (a) (b)
112 You look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refractionn To left (Fig. 34-57). Because you view with two eyes, which intercept different rays of light from the coin, you per- To right eye eye Air ceive the coin to be where extensions of the intercepted rays cross, at depth d, instead of d. Assuming that the intercepted rays in Fig. 34-57 are close to a vertical axis through the coin, show that d, = din. (Hint: Use the small-angle approximation sin 0 tan 6- 0.) Figure 34-57 Problem 112.
Flying Circus of Physics Rainbow. Figure (a) shows a light ray entering and then leaving a falling, spherical raindrop after one internal re-flection (see Figure (b) below). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation de (a) is equation beneath true eccy-180"+28-48 where 8, is the angle of incidence of the ray on the drop and 8, is the angle of refraction of the ray within the crop? Using Snell's law, substitute for e, in terms of 9; and the index of refraction of the water. Then, on a graphing calculator or with a computer graphing package.graph 6de, versus 8 for the range of possible 8; values and for n = 1.331 for red light and n = 1.343 for blue light. The red-light curve and the blue-light curve have different minima, which means that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that color's angle of minimum deviation is especially bright because…
•• ENGINEERING APPLICATION An optical fiber allows rays of light to propagate long distances by using total internal reflec- tion. Optical fibers are used extensively in medicine and in digital communications. As shown in Figure 31-58 the fiber consists of a core material that has an index of refraction n, and radius b sur- rounded by a cladding material that has an index of refraction n3 < n2. The numerical aperture of the fiber is defined as sine, where 0, is the angle of incidence of a ray of light that impinges on the center of the end of the fiber and then reflects off the core- cladding interface just at the critical angle. Using the figure as a guide, show that the numerical aperture is given by sine, = Vn3 - n? assuming the ray is initially in air. Hint: Use of the Pythagorean theorem may be required. 44
• During a daytime football game you notice that a player’s reflective helmet forms an image of the Sun 4.8 cm behind the surface ofthe helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?
Can a light ray traveling in air be totally reflected when itstrikes a smooth water surface if the incident angle is chosencorrectly? Explain.
2 In Fig. 34-26, stick figure O Figure 34-25 Question 1. stands in front of a spherical mirror that is mounted within the boxed re- gion; the central axis through the 20 24 mirror is shown. The four stick fig- A ures Iį to l4 suggest general loca- tions and orientations for the im- L--- ages that might be produced by the mirror. (The figures are only sketched in; neither their heights nor their distances from the mirror are drawn to scale.) (a) Which of the stick figures could not possibly represent images? Of the possible images, (b) which would be due to a concave mirror, (c) which would be due to a convex mirror, (d) which would be virtual, and (e) which would involve negative magnification? Figure 34-26 Questions 2 and 10.

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