PHYS 2212 Module 13 Self Assessment Practice Problems

13.1
An electromagnetic wave with a frequency of 4.90 x 10¹⁴ Hz propagates with a speed of 2.25 x 10⁸ m/s in a certain piece of glass.
(a) Find the wavelength of the wave in the glass.
(b) Find the wavelength of a wave of the same frequency propagating in air.
(c) Find the index of refraction n of the glass for an electromagnetic wave with this frequency.
(d) Find the dielectric constant for glass at this frequency, assuming that the relative permeability is unity (= 1).
Answer: (a) 459 nm (b) 612 nm (c) 1.33 (d) 1.78

13.2
The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 400 nm (violet) to 700 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina.
(a) What are the ranges of the wavelength of the light just as it approaches the retina within the vitreous humor?
(b) What are the ranges of the frequency of the light just as it approaches the retina within the vitreous humor?
(c) What is the speed of the light just as it approaches the retina within the vitreous humor?
Answer: (a) 298 nm to 522 nm (b) 7.5 x 10¹⁴ Hz to 4.3 x 10¹⁴ Hz (c) 2.24 x 10⁸ m/s

13.3
A laser beam shines along the surface of a block of transparent material. Half of the beam goes straight to a detector, while the other half travels through the block and then hits the detector. The time delay between the arrival of the two light beams at the detector is 6.25 ns. What is the index of refraction of this material?
Answer: 1.71

13.4
Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?
Answer: 39.4°

13.5
A parallel beam of light in air makes an angle of 47.5° with the surface of a glass plate having a refractive index of 1.66.
(a) What is the angle between the reflected part of the beam and the surface of the glass?
(b) What is the angle between the refracted beam and the surface of the glass?
Answer: (a) 47.5° (b) 66°

13.6
You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. a). The glass is a thin-walled, hollow cylinder 16.0 cm high. The diameter of the top and bottom of the glass is 8.0 cm. While you keep your eye in the same position, a friend fills the glass with a transparent liquid, and you then see a dime that is lying at the center of the bottom of the glass (Fig. b). What is the index of refraction of the liquid?
Answer: 1.85

13.6

You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. a). The glass is a thin-walled, hollow cylinder 16.0 cm high. The diameter of the top and bottom of the glass is 8.0 cm. While you keep your eye in the same position, a friend fills the glass with a transparent liquid, and you then see a dime that is lying at the center of the bottom of the glass (Fig. b). What is the index of refraction of the liquid?

Answer: 1.85

13.7
As shown in the figure, a layer of water (n = 1.33) covers a slab of material X in a beaker. A ray of light traveling upwards follows the path indicated.
(a) Using the information on the figure, find the index of refraction of material X.
(b) Find the angle the light makes with the normal in the air.
Answer: (a) 2.34 (b) 81°

13.8
A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water.
(a) What is the largest angle with respect to the normal that the ray can make at the ice-water interface and still pass out into the air above the ice?
(b) What is this angle after the ice melts?
Answer: (a) 48° (b) 48°

13.9
Light of original intensity I₀ passes through two ideal polarizing filters having their polarizing axes oriented as shown. You want to adjust the angle φ so that the intensity at point P is equal to I₀/10.
(a) If the original light is unpolarized, what should φ be?
(b) If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should φ be?
Answer: (a) 63° (b) 71.6°

13.10
The refractive index of a certain glass is 1.66. For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in
(a) air?
(b) water?
Answer: (a) 59° (b) 51°