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Chapter 25 | Geometric Optics
Problems & Exercises
25.1 The Ray Aspect of Light
1. Suppose a man stands in front of a mirror as shown in
Figure 25.50. His eyes are 1.65 m above the floor, and the
top of his head is 0.13 m higher. Find the height above the
floor of the top and bottom of the smallest mirror in which he
can see both the top of his head and his feet. How is this
distance related to the man’s height?
Figure 25.52 A flat mirror neither converges nor diverges light rays. Two
rays continue to diverge at the same angle after reflection.
25.3 The Law of Refraction
5. What is the speed of light in water? In glycerine?
6. What is the speed of light in air? In crown glass?
7. Calculate the index of refraction for a medium in which the
8
speed of light is 2.012×10 m/s , and identify the most
likely substance based on Table 25.1.
8. In what substance in Table 25.1 is the speed of light
2.290×10 8 m/s ?
Figure 25.50 A full-length mirror is one in which you can see all of
yourself. It need not be as big as you, and its size is independent of your
distance from it.
25.2 The Law of Reflection
2. Show that when light reflects from two mirrors that meet
each other at a right angle, the outgoing ray is parallel to the
incoming ray, as illustrated in the following figure.
9. There was a major collision of an asteroid with the Moon in
medieval times. It was described by monks at Canterbury
Cathedral in England as a red glow on and around the Moon.
How long after the asteroid hit the Moon, which is
3.84×10 5 km away, would the light first arrive on Earth?
10. A scuba diver training in a pool looks at his instructor as
shown in Figure 25.53. What angle does the ray from the
instructor’s face make with the perpendicular to the water at
the point where the ray enters? The angle between the ray in
the water and the perpendicular to the water is 25.0º .
Figure 25.51 A corner reflector sends the reflected ray back in a
direction parallel to the incident ray, independent of incoming direction.
3. Light shows staged with lasers use moving mirrors to swing
beams and create colorful effects. Show that a light ray
reflected from a mirror changes direction by 2θ when the
mirror is rotated by an angle
θ.
Figure 25.53 A scuba diver in a pool and his trainer look at each other.
4. A flat mirror is neither converging nor diverging. To prove
this, consider two rays originating from the same point and
diverging at an angle θ . Show that after striking a plane
mirror, the angle between their directions remains
θ.
11. Components of some computers communicate with each
other through optical fibers having an index of refraction
n = 1.55 . What time in nanoseconds is required for a signal
to travel 0.200 m through such a fiber?
172
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