Download Chapter 26: Geometrical Optics

Chapter 26: Geometrical Optics
Answers to Even-Numbered Conceptual Questions
2.
Three images are formed of object B. One extends from (–3 m, 1 m) to (–3 m, 2 m) to (– 4 m, 2 m). Another
image forms an “L” from (3 m, –1 m) to (3 m, –2 m) to (4 m, –2 m). Finally, the third image extends from
(–3 m, –1 m) to (–3 m, –2 m) to (– 4 m, –2 m).
4.
The concave side of the dish collects the parallel rays coming from a geosynchronous satellite and focuses
them at the focal point of the dish. The convex side of the dish would send the parallel rays outward on
divergent paths. The situation is analogous to that of light in an optical telescope.
6.
No. Light bends toward the normal when it enters a medium in which its speed of propagation is less than it
was in the first medium – as when light passes from air to water. On the other hand, light bends away from the
normal if it enters a medium in which its speed is increased – as when light passes from water to air.
8.
You are actually seeing light from the sky, which has been bent upward by refraction in the low-density air
near the hot ground. See figure 26-23 for a case where one would see a tree reflected in the "pool of water."
10.
The Sun is already well below the horizon when you see it setting. The reason is that as the Sun’s light enters
the atmosphere from the vacuum of space, it is bent toward the normal; that is, toward the surface of Earth.
Therefore, the light from the Sun can still reach us even when a straight line from our eyes to the Sun would
go below the horizon.
12.
The oil used in the bottle to the left has an index of refraction that is equal to the index of refraction of the
glass in the eye dropper. Therefore, light is undeflected when it passes from the oil to the glass or from the
glass to the oil. Because light propagates the same as if the eye dropper were not present, the dropper is
invisible.
14.
Note that the word “SECRET,” which is in red, is inverted. On the other hand, the word “CODE,” which is in
blue, appears not to be inverted. One might think that the different index of refraction for blue light versus red
light is responsible for this behavior, but recall that we said the word “CODE” appears not to be inverted. In
fact, it is inverted, just like the word “SECRET,” but because all of its letters have a vertical symmetry, it
looks the same when inverted.
Chapter 27: Optical Instruments
Answers to Even-Numbered Conceptual Questions
2.
No. The lens will still show a complete image, though you may have to move your head more from side to
side to see it all.
4.
The reason things look blurry underwater is that there is much less refraction of light when it passes from
water to your cornea than when it passes from air to your cornea. Therefore, your eyes simply aren’t
converging light enough when they are in water. Since farsightedness is caused when your eyes don’t
converge light as much as they should (see Figure 27-11), this can be considered as an extreme case of
farsightedness.
6.
Yes, it matters. A simple magnifier is nothing more than a convex lens. As we can see from Figure 26-35, a
convex lens forms an enlarged (magnified) image only when the object is closer to the lens than its focal
length.
8.
No. Chromatic aberration occurs in lenses because light of different frequency refracts by different amounts.
In the case of a mirror, however, all light—regardless of its frequency—obeys the same simple law of
reflection; namely, that the angle of reflection is equal to the angle of incidence. Since light of all colors is
bent in the same way by a mirror, there is no chromatic aberration.
Chapter 28: Physical Optics: Interference and Diffraction
Answers to Even-Numbered Conceptual Questions
2.
If the slit spacing, d, were less than the wavelength, λ, the condition for a bright fringe (equation 28-1) could
be satisfied only for the central bright fringe (m = 0). For nonzero values of m there are no solutions, because
sinθ cannot be greater than one. In addition, equation 28-2 shows that if d is greater than λ/2, though still less
than λ, there will be only one dark fringe on either side of the central bright fringe. If d is less than λ/2, no dark
fringes will be observed.
4.
The locations of bright and dark fringes depend on the wavelength of light. Therefore, if white light is used in
a two-slit experiment, each bright fringe will show some separation into colors, giving a “rainbow” effect.
6.
Submerging the two-slit experiment in water would reduce the wavelength of the light from λ to λ/n, where n =
1.33 is the index of refraction of water. Therefore, the angles to all the bright fringes would be reduced, as we
can see from equation 28-1. It follows that the two-slit pattern of bright fringes would be more tightly spaced
in this case.
8.
One possible reason is that one of the films may have an index of refraction greater than that of glass, whereas
the other may have an index of refraction that is less than that of glass. If this is the case, the phase change in
reflection from the film-glass interface will be different for the two films. This, in turn, would result in
different colors appearing in the reflected light.
10.
A cat’s eye would give greater resolution in the vertical direction, because the effective aperture is greater in
that direction. As shown in equation 28-14, the greater the aperture, D, the smaller the angle, θ, and the greater
the resolution.
12.
In an iridescent object, the color one sees is determined by constructive and destructive interference. The
conditions for interference, however, depend on path length, and path length depends on the angle from which
one views the system. This is analogous to viewing a two-slit system from different angles and seeing
alternating regions of constructive and destructive interference. A painted object, on the other hand, simply
reflects light of a given color in all directions.