Content check — College Physics, Chapter 25: Geometric Optics

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 25: Geometric Optics

31 problems · 3 figures

Suppose a man stands in front of a mirror as shown in Figure 25.48. 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?

A man standing in front of a mirror on a wall at a distance of several feet. The mirror’s top is at eye level, but its bottom is only waist high. Arrows illustrate how the man can see his reflection from head to toe in the mirror. — Figure 25.48 in the book ↗

Answer

Top

1 . 715 m

from floor, bottom

0 . 825 m

from floor. Height of mirror is

0 . 890 m

, or precisely one-half the height of the person.

25-5 §25.3 source ↗

What is the speed of light in water? In glycerine?

Answer

$2 . 25 \times 10^{8} m/s$ in water

$2 . 04 \times 10^{8} m/s$ in glycerine

25-7 §25.3 source ↗

Calculate the index of refraction for a medium in which the speed of light is

2.012 \times 10^{8} m/s

, and identify the most likely substance based on Table 25.1.

Table 25.1 Index of Refraction in Various Media in the book ↗

Medium	n
*Gases at $0ºC$ , 1 atm*
Air	1.000293
Carbon dioxide	1.00045
Hydrogen	1.000139
Oxygen	1.000271
Liquids at $20ºC$
Benzene	1.501
Carbon disulfide	1.628
Carbon tetrachloride	1.461
Ethanol	1.361
Glycerine	1.473
Water, fresh	1.333
Solids at $0ºC$
Diamond	2.419
Fluorite	1.434
Glass, crown	1.52
Glass, flint	1.66
Ice at $0ºC$	1.309
Magnesium Fluoride	1.38
Polystyrene	1.49
Plexiglas	1.51
Quartz, crystalline	1.544
Quartz, fused	1.458
Sodium chloride	1.544
Zircon	1.923

Answer

1.490

, polystyrene

25-9 §25.3 source ↗

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 \times 10^{5} km

away, would the light first arrive on Earth?

Answer

1 . 28 s

25-11 §25.3 source ↗

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?

Answer

1.03 ns

25-13 §25.3 source ↗

Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of

45 . 0º

, and you observe the angle of refraction to be

40 . 3º

. What is the index of refraction of the substance and its likely identity?

Answer

n = 1 . 46

, fused quartz

25-17 §25.3 source ↗

Unreasonable Results

Suppose light travels from water to another substance, with an angle of incidence of $10 . 0º$ and an angle of refraction of $14 . 9º$ . (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Answer

(a) 0.898

(b) Can’t have $n < 1 . 00$ since this would imply a speed greater than $c$ .

25-19 §25.3 source ↗

Unreasonable Results

Light traveling from water to a gemstone strikes the surface at an angle of $80 . 0º$ and has an angle of refraction of $15 . 2º$ . (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Answer

(a) $\frac{c}{5.00}$

(b) Speed of light too slow, since index is much greater than that of diamond.

25-22 §25.4 source ↗

An optical fiber uses flint glass clad with crown glass. What is the critical angle?

Answer

66 . 3º

25-24 §25.4 source ↗

Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is

45 . 0º

, what must be the minimum index of refraction of the material from which the reflector is made?

Answer

> 1.414

25-26 §25.4 source ↗

A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown in Figure 25.53. What is the index of refraction for the liquid and its likely identification?

A light ray travels from an object placed in a denser medium n1 at 15.0 centimeter from the boundary and on hitting the boundary gets totally internally reflected with theta c as critical angle. The horizontal distance between the object and the point of incidence is 13.4 centimeters. — Figure 25.53 in the book ↗

Answer

1.50, benzene

25-29 §25.5 source ↗

A beam of white light goes from air into water at an incident angle of

75 . 0º

. At what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?

Answer

46 . 5º, red; 46 . 0º, violet

25-31 §25.5 source ↗

(a) A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a

30 . 0º

incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?

Answer

(a) $0 . 043º$

(b) $1 . 33 m$

25-33 §25.5 source ↗

A ray of 610 nm light goes from air into fused quartz at an incident angle of

55 . 0º

. At what incident angle must 470 nm light enter flint glass to have the same angle of refraction?

Answer

71.3º

25-35 §25.5 source ↗

A narrow beam of white light enters a prism made of crown glass at a

45 . 0º

incident angle, as shown in Figure 25.55. At what angles,

θ_{R}

and

θ_{V}

, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism?

A blue incident light ray at an angle of incidence equal to 45 degrees falls on an equilateral triangular prism with angles each equal to 60 degrees. On falling onto the first surface, the ray refracts and splits into red and violet rays. These rays falling onto the second surface and emerge from the prism. Red with 660 nanometers and violet with 410 nanometers. — Figure 25.55 in the book ↗

Answer

53.5º, red;

55.2º, violet

25-37 §25.6 source ↗

Your camera’s zoom lens has an adjustable focal length ranging from 80.0 to 200 mm. What is its range of powers?

Answer

5.00 to 12.5 D

25-39 §25.6 source ↗

You note that your prescription for new eyeglasses is –4.50 D. What will their focal length be?

Answer

- 0.222 m

25-41 §25.6 source ↗

A certain slide projector has a 100 mm focal length lens. (a) How far away is the screen, if a slide is placed 103 mm from the lens and produces a sharp image? (b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the image? Explicitly show how you follow the steps in the Problem-Solving Strategy for lenses.

Answer

(a) 3.43 m

(b) 0.800 by 1.20 m

25-42 §25.6 source ↗

A doctor examines a mole with a 15.0 cm focal length magnifying glass held 13.5 cm from the mole (a) Where is the image? (b) What is its magnification? (c) How big is the image of a 5.00 mm diameter mole?

Answer

(a) $- 1 . 35 m$ (on the object side of the lens).

(b) $+ 10 . 0$

25-43 §25.6 source ↗

How far from a piece of paper must you hold your father’s 2.25 D reading glasses to try to burn a hole in the paper with sunlight?

Answer

44.4 cm

25-45 §25.6 source ↗

A camera lens used for taking close-up photographs has a focal length of 22.0 mm. The farthest it can be placed from the film is 33.0 mm. (a) What is the closest object that can be photographed? (b) What is the magnification of this closest object?

Answer

(a) 6.60 cm

(b) –0.500

25-47 §25.6 source ↗

(a) What is the focal length of a magnifying glass that produces a magnification of 3.00 when held 5.00 cm from an object, such as a rare coin? (b) Calculate the power of the magnifier in diopters. (c) Discuss how this power compares to those for store-bought reading glasses (typically 1.0 to 4.0 D). Is the magnifier’s power greater, and should it be?

Answer

(a) $+ 7 . 50 cm$

(b) $13 . 3 D$

25-49 §25.6 source ↗

In Example 25.7, the magnification of a book held 7.50 cm from a 10.0 cm focal length lens was found to be 4.00. (a) Find the magnification for the book when it is held 8.50 cm from the magnifier. (b) Do the same for when it is held 9.50 cm from the magnifier. (c) Comment on the trend in m as the object distance increases as in these two calculations.

Example 25.7 Image Produced by a Magnifying Glass in the book ↗

Answer

(a) +6.67

(b) +20.0

(c) The magnification increases without limit (to infinity) as the object distance increases to the limit of the focal distance.

25-51 §25.6 source ↗

A camera with a 100 mm focal length lens is used to photograph the sun and moon. What is the height of the image of the sun on the film, given the sun is

1.40 \times 10^{6} km

in diameter and is

1.50 \times 10^{8} km

away?

Answer

- 0 . 933 mm

25-53 §25.7 source ↗

What is the focal length of a makeup mirror that has a power of 1.50 D?

Answer

+0.667 m

25-55 §25.7 source ↗

(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature. (b) What is its power in diopters?

Answer

(a) $–1.5 \times 10^{–2} m$

(b) $–66.7 D$

25-57 §25.7 source ↗

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors.

Answer

+0.360 m (concave)

25-59 §25.7 source ↗

An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.167 cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by optometrists to measure the curvature of the cornea for contact lens fitting. The instrument used is called a keratometer, or curve measurer.)

Answer

(a) +0.111

(b) -0.334 cm (behind “mirror”)

25-61 §25.7 source ↗

Show that for a flat mirror

h_{i} = h_{o}

, knowing that the image is a distance behind the mirror equal in magnitude to the distance of the object from the mirror.

Answer

m = \frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}} = - \frac{- d_{o}}{d_{o}} = \frac{d_{o}}{d_{o}} = 1 \Rightarrow h_{i} = h_{o}

25-63 §25.7 source ↗

Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in

{W/m}^{2}

projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 W and has an area of

100 {cm}^{2}

, and that half of the radiated power is reflected and focused by the mirror.

Answer

6.82 k {W/m}^{2}

25-65 §25.7 source ↗

Critical Thinking Light composed of multiple frequencies passes through crown glass. (a) How much faster does the violet component of the light with a wavelength of 410 nm travel in the crown glass than the component of orange light with a wavelength of 610 nm? (b) In a mechanical situation with friction, the longer one surface moves relative to the other, the more the friction acts, slowing the relative motion during the process. Is this the same for light in a medium? (c) In a mechanical situation, it is possible for friction to stop the motion if it occurs over a long enough path. Is this the same for light in a medium? (d) In a mechanical friction situation, once the object slows it will not increase in speed once the friction no longer acts unless another force is present. If a light ray exits a medium into a vacuum, will it go back to a speed of c even though that would be an increase in speed not caused by an additional force?

Answer

(a) $\begin{array}{l} v_{610} = \frac{3.00 \times 10^{8}}{1.530} m/s, v_{410} = \frac{3.00 \times 10^{8}}{1.514} m/s \\ 3 .00 \times 10^{8} \frac{1}{1.514} - \frac{1}{1.530} m/s = 2.07 \times 10^{6} m/s \end{array}$

(b) No.

(d) Yes.

Loading chapter 26…

Problems and answers are adapted from College Physics 2e by Paul Peter Urone, Roger Hinrichs, Kim Dirks and Manjula Sharma, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.