# Unit 7 Problem Set

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8.1     When an electromagnetic wave travels from one medium to another wit a different speed of propagation,
the frequency of the wave remains the same. Its wavelength, however changes. (a) If the wave speed
decreases, does the wavelength increase or decrease? Explain. (b) Consider the case where the wave speed
decreases from c to ¾ c. By what factor does the wavelength change?

8.2    ULF (ultra low frequency) electromagnetic waves, produced in the depths of outer space, have been
observed with wavelengths in excess of 29 million kilometers. What is the period of such a wave?

8.3    You are 1.8 m tall and stand 3.0 m from a plane mirror that extends vertically upward from the floor.
On the floor 1.5 m in front of the mirror is a small table, 0.80 m high. What is the minimum height the mirror
must have for you to be able to see the top of the table in the mirror?

8.4     For a corner reflector to be effective, its surfaces must be precisely perpendicular. Suppose the surfaces
of a corner reflector left on the Moon’s surface by the Apollo astronauts formed a 90.001o angle with each
other. If a laser beam is bounced back to Earth from this reflector, how far (in kilometers) from its starting
point will the reflected beam strike Earth? For simplicity assume the beam reflects from only two side of the
reflector, and that it strikes the first surface at precisely 45o.

8.5    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 of the helmet. What is the radius of curvature of the helmet, assuming it to be
roughly spherical?

8.6      A 2.00 cm high object is placed 10.0 cm in front of a concave mirror. If the image is 5.00 cm high and
virtual, what is the focal length of the mirror?

8.7     A pond with a total depth (ice + water) of 3.00 m is covered by a transparent layer of ice (n=1.31), with
a thickness of 0.32 m. Find the time required for light to travel vertically from the surface of the ice to the
bottom of the pond (n=1.33 for water).

8.8     A submerged scuba diver looks up toward the calm surface of a freshwater lake and notes that the Sun
appears to be 35o from the vertical. The diver’s friend is standing on the shore of the lake. At what angle above
the horizon does the friend see the sun (n=1.33 for water)

8.9     Light is refracted as it travels from a point A in medium 1 to a point B in medium 2. If the index of
refraction is 1.33 in medium 1 and 1.51 in medium 2, how long does it take light to go from A to B, assuming it
travels 331 cm in medium 1 and 151 cm in medium 2?

8.10 An observer is positioned so that the far edge of the bottom of an empty glass is just visible. When the
glass is filled to the top with water, the center of the bottom of the glass is just visible to the observer. (a) Draw
two diagrams to show the pathway of light in each situation. (b) Find the height, H, of the glass, given that its
width is W=6.2 cm.

8.11 A lens for a 35 mm camera has a focal length give by f=45 mm. (a) How close to the film should the
lens be placed to form a sharp image of an object that is 5.0 m away? (b) What is the magnification of the
image on the film?

8.12 An object is located to the left of a concave lens whose focal length is -36 cm. The magnification
produced by the lens is m = 1 . (a) To decrease the magnification to m= 1 , should the object be moved closer to
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the lens or farther away? (b) Calculate the distance through which the object should be moved.
8.13 A ray of light enters the long side of a 45o-90o-45 prism and undergoes two total internal reflections.
The result is a reversal in the ray’s direction of propagation. Find the minimum value of the prism’s index of
refraction, n, for these internal reflections to be total.

90o

45o                      45o

8.14 Albert is nearsighted, and without his glasses he can only focus on objects less than 2.2 m away. (a)
Are Albert’s eyeglasses concave or convex? Explain. (b) To correct Albert’s nearsightedness, his eyeglasses
must produce a virtual, upright image at a distance of 2.2 m when viewing an infinitely distant object. What is
the focal length of Albert’s eyeglasses?

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