College Physics: A Strategic Approach

Randall D. Knight, Brian Jones, Stuart Field

Chapter 18

Ray Optics - all with Video Answers

Educators

Chapter Questions

Problem 1

A 5.0-ft-tall girl stands on level ground. The sun is $25^{\circ}$ above the horizon. How long is her shadow?

Sheh Lit Chang

Sheh Lit Chang

University of Washington

Problem 2

In Figure P18.2, the compact flame of a candle casts a 15 -cm-high shadow of a 8.2-cm-tall tree cutout. The candle is $3.2 \mathrm{cm}$ from the cutout; how far is the candle from the wall?

Sheh Lit Chang

University of Washington

Problem 3

A point source of light illuminates an aperture $2.00 \mathrm{m}$ away. A 12.0 -cm-wide bright patch of light appears on a screen $1.00 \mathrm{m}$ behind the aperture. How wide is the aperture?

Sheh Lit Chang

University of Washington

Problem 4

The mirror in Figure $\mathrm{P} 18.4$ deflects a horizontal laser beam by $60^{\circ} .$ What is the angle $\phi ?$

Sheh Lit Chang

University of Washington

Problem 5

It is $165 \mathrm{cm}$ from your eyes to your toes. You're standing $200 \mathrm{cm}$ in front of a tall mirror. How far is it from your eyes to the image of your toes?

Rodger Claar

Numerade Educator

Problem 6

Figure $\mathrm{P} 18.6$ shows an object $\mathrm{O}$ in front of a plane mirror. Draw rays from the object that reflect from the mirror to determine from which locations $\mathrm{A}-\mathrm{D}$ the object's image is visible.

Sheh Lit Chang

University of Washington

Problem 7

A ray of light enters the region between two mirrors, as shown in Figure $\mathrm{P} 18.7$. How many times does the light reflect before exiting the space between the two mirrors?

Sheh Lit Chang

University of Washington

Problem 8

You are standing $1.5 \mathrm{m}$ from a mirror, and you want to use a classic camera to take a photo of yourself. This camera requires you to select the distance of whatever you focus on. What distance do you choose?

Sheh Lit Chang

University of Washington

Problem 9

Starting $3.5 \mathrm{m}$ from a department store mirror, Suzanne walks toward the mirror at $1.5 \mathrm{m} / \mathrm{s}$ for $2.0 \mathrm{s}$. How far is Suzanne from her image in the mirror after $2.0 \mathrm{s}$ ?

Sheh Lit Chang

University of Washington

Problem 10

The lightbulb in Figure P18.10 is $50 \mathrm{cm}$ from a mirror. It emits 1.5 W of visible light. A small barrier blocks the direct rays of light from the bulb from reaching a sensor $70 \mathrm{cm}$ to the right, but not the reflected rays. What is the light intensity at the sensor?

Sheh Lit Chang

University of Washington

Problem 11

A ray of light impinges on a mirror as shown in Figure $\mathrm{P} 18.11 .$ A second mirror is fastened at $90^{\circ}$ to
the first. After striking both mirrors, at what angle relative to the incoming ray does the outgoing ray emerge?

Sheh Lit Chang

University of Washington

Problem 12

An underwater diver sees the sun $50^{\circ}$ above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver?

Vishal Gupta

Numerade Educator

Problem 13

A laser beam in air is incident on a liquid at an angle of $37^{\circ}$ with respect to the normal. The laser beam's angle in the liquid is $26^{\circ} .$ What is the liquid's index of refraction?

Rodger Claar

Numerade Educator

Problem 14

The sun is $60^{\circ}$ above the horizon. Rays from the sun strike the still surface of a pond and cast a shadow of a stick that is stuck in the sandy bottom of the pond. If the stick is $10 \mathrm{cm}$ tall, how long is the shadow?

Sheh Lit Chang

University of Washington

Problem 15

A 1.0 -cm-thick layer of water stands on a horizontal slab of glass. A light ray in the air is incident on the water $60^{\circ}$ from the normal. After entering the glass, what is the ray's angle from the normal?

Sheh Lit Chang

University of Washington

Problem 16

Figure $\mathrm{P} 18.16$ shows a ray of light entering an equilateral prism, with all sides and angles equal to each other. The ray traverses the prism parallel to the bottom and emerges at the same angle at which it entered. If $\theta=40^{\circ}$, , what is the index of refraction of
the prism?

Sheh Lit Chang

University of Washington

Problem 17

A 4.0-m-wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is $20^{\circ}$ above the horizon. How deep is the pool?

Sheh Lit Chang

University of Washington

Problem 18

You are on a snorkeling trip. Deep below the water, you look up at the surface of the water. Right at sunset, at what angle from the vertical do you see the sun?

Sheh Lit Chang

University of Washington

Problem 19

A ray of light traveling through air encounters a $1.2-\mathrm{cm}$ -thick sheet of glass at a $35^{\circ}$ angle of incidence. How far does the light ray travel in the glass before emerging on the far side?

Sheh Lit Chang

University of Washington

Problem 20

A thin glass rod is submerged in oil. What is the critical angle for light traveling inside the rod?

Rodger Claar

Numerade Educator

Problem 21

A light ray travels inside a horizontal plate of glass, striking its upper surface at an angle of incidence of $60^{\circ} .$ This ray is totally internally reflected at the glass-air boundary. A liquid is then poured on top of the glass. What is the largest index of refraction that the liquid could have such that the ray is still totally internally reflected?

Sheh Lit Chang

University of Washington

Problem 22

A typical diamond is cut as shown in Figure $\mathrm{P} 18.22$. A ray of light has entered the flat window at the top of the diamond perpendicular to the surface, as shown in the figure. Analyze the path of the ray for the next two interactions with the surfaces of the diamond.

Sheh Lit Chang

University of Washington

Problem 23

A light ray travels inside a block of sodium fluoride that has index of refraction $n=1.33$ as shown in Figure $\mathrm{P} 18.23 .$ The ray strikes the vertical wall at the critical angle, totally reflects, and then emerges into the air above the block. What is the angle $\theta_{2}$ at which the ray emerges?

Sheh Lit Chang

University of Washington

Problem 24

Canola oil is less dense than water, so it floats on water, but its index of refraction is $1.47,$ higher than that of water. When you are adding oil and water to a bottle to make salad dressing, you notice a silvery reflection of light from the boundary between the oil and water. What is the critical angle for light going from the oil into the water?

Sheh Lit Chang

University of Washington

Problem 25

A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be $2.0 \mathrm{cm}$ within the plastic. What is the beetle's actual distance beneath the surface?

Rodger Claar

Numerade Educator

Problem 26

The composition of the ancient atmosphere can be determined by analyzing bubbles of air trapped in amber, which is fossilized tree resin. (This is one way we know that the air in the time of the dinosaurs was richer in oxygen than our current atmosphere.) An air bubble appears to be $7.2 \mathrm{mm}$ below the flat surface of a piece of amber, which has index of refraction $1.54 .$ How long a needle is required to reach the bubble?

Sheh Lit Chang

University of Washington

Problem 27

A fish in a flat-sided aquarium sees a can of fish food on the counter. To the fish's eye, the can looks to be $30 \mathrm{cm}$ outside the aquarium. What is the actual distance between the can and the aquarium? (You can ignore the thin glass wall of the aquarium.)

Rodger Claar

Numerade Educator

Problem 28

A 1.8-m-tall diver is standing completely submerged on the bottom of a swimming pool, in $3.0 \mathrm{m}$ of water. You are sitting on the end of the diving board, almost directly over her. How tall does the diver appear to be?

Sheh Lit Chang

University of Washington

Problem 29

A swim mask has a pocket of air between your eyes and the flat glass front.
a. If you look at a fish while swimming underwater with a swim mask on, does the fish appear closer or farther than it really is? Draw a ray diagram to explain.
b. Does the fish see your face closer or farther than it really is? Draw a ray diagram to explain.

Sheh Lit Chang

University of Washington

Problem 30

An object is $30 \mathrm{cm}$ in front of a converging lens with a focal length of $10 \mathrm{cm} .$ Use ray tracing to determine the location of the image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 31

An object is $6.0 \mathrm{cm}$ in front of a converging lens with a focal length of $10 \mathrm{cm} .$ Use ray tracing to determine the location of the image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 32

In order to start a fire, a camper turns a lens toward the sun to focus its rays on a piece of wood. The lens has a $10 \mathrm{cm}$ focal length. Draw a ray diagram of the lens and the incoming light rays to show where the wood should be placed for the best effect.

Sheh Lit Chang

University of Washington

Problem 33

You are using a converging lens to look at a splinter in your finger. The lens has a $9.0 \mathrm{cm}$ focal length, and you place the splinter $6.0 \mathrm{cm}$ from the lens. How far from the lens is the image? What is the magnification?

Prabhat Tyagi

Numerade Educator

Problem 34

You are using a converging lens to look at a splinter in your finger. The lens has a $9.0 \mathrm{cm}$ focal length, and you place the splinter $6.0 \mathrm{cm}$ from the lens. How far from the lens is the image? What is the magnification?

Sheh Lit Chang

University of Washington

Problem 35

An object is $15 \mathrm{cm}$ in front of a diverging lens with a focal length of $-10 \mathrm{cm} .$ Use ray tracing to determine the location of the image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 36

A 2.0 -cm-tall object is located $8.0 \mathrm{cm}$ in front of a converging lens with a focal length of $10 \mathrm{cm}$. Use ray tracing to determine the location and height of the image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 37

A converging cosmetic mirror has a focal length of $40 \mathrm{cm} .$ A $5-\mathrm{cm}-\mathrm{long}$ mascara brush is held upright $20 \mathrm{cm}$ from the mirror. Use ray tracing to determine the location and height of its image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 38

A photographer took this image of himself in a converging mirror. Give some thought to what you are seeing here: One of the hands is his left hand; the other is the image of his left hand. Given the relative sizes and positions of his hand and the image of his hand, how far from the mirror did he place his hand to take this photo? Express your answer in terms of $f$, the mirror's focal length.

Sheh Lit Chang

University of Washington

Problem 39

A lightbulb is $60 \mathrm{cm}$ from a converging mirror with a focal length of $20 \mathrm{cm} .$ Use ray tracing to determine the location of its image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 40

A flashlight uses a small lightbulb placed in front of a converging mirror. The light from the bulb should reflect from the mirror and emerge as a tight beam of light-a series of parallel rays. Where should the bulb be placed relative to the mirror?

Sheh Lit Chang

University of Washington

Problem 41

A dentist uses a curved mirror to view the back side of teeth on the upper jaw. Suppose she wants an erect image with a magnification of 2.0 when the mirror is $1.2 \mathrm{cm}$ from a tooth. (Treat this problem as though the object and image lie along a straight line.) Use ray tracing to decide whether a converging or diverging mirror is needed, and to estimate its focal length.

Sheh Lit Chang

University of Washington

Problem 42

A diverging mirror, like the passenger-side rearview mirror on a car, has a focal length of $-2.0 \mathrm{m}$. An object is $4.0 \mathrm{m}$ from the mirror. Use ray tracing to determine the location of its image. Is the image upright or inverted? Is it real or virtual?

Sheh Lit Chang

University of Washington

Problem 43

An object is $12 \mathrm{cm}$ in front of a diverging mirror. The mirror creates an image that is $75 \%$ as tall as the object. Use ray tracing to find the distance of the focal point from the mirror.

Sheh Lit Chang

University of Washington

Problem 44

Calculate the image position and height.
A 2.0 -cm-tall object is $40 \mathrm{cm}$ in front of a converging lens that has a $20 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 45

Calculate the image position and height.
A 1.0 -cm-tall object is $10 \mathrm{cm}$ in front of a converging lens that has a $30 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 46

Calculate the image position and height.
A 2.0-cm-tall object is 15 cm in front of a converging lens that has a $20 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 47

Calculate the image position and height.
A $1.0-\mathrm{cm}$ -tall object is $75 \mathrm{cm}$ in front of a converging lens that has a $30 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 48

Calculate the image position and height.
A $2.0-\mathrm{cm}$ -tall object is $15 \mathrm{cm}$ in front of a diverging lens that has a $-20 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 49

Calculate the image position and height.
A $1.0-\mathrm{cm}$ -tall object is $60 \mathrm{cm}$ in front of a diverging lens that has a -30 cm focal length.

Sheh Lit Chang

University of Washington

Problem 50

Calculate the image position and height.
A $3.0-\mathrm{cm}$ -tall object is $15 \mathrm{cm}$ in front of a diverging mirror that has a $-25 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 51

Calculate the image position and height.
A $3.0-\mathrm{cm}$ -tall object is $45 \mathrm{cm}$ in front of a diverging mirror that has a $-25 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 52

Calculate the image position and height.
A 3.0 -cm-tall object is $15 \mathrm{cm}$ in front of a converging mirror that has a $25 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 53

Calculate the image position and height.
A 3.0 -cm-tall object is $45 \mathrm{cm}$ in front of a converging mirror that has a $25 \mathrm{cm}$ focal length.

Sheh Lit Chang

University of Washington

Problem 54

Calculate the image position and height.
A toy insect viewer for kids consists of a plastic container with a lens in the lid. The lid is $12 \mathrm{cm}$ from the bottom of the container. The lens produces a magnified image of an insect on the bottom of the container. If the magnification is $4.0,$ what is the focal length of the lens?

Sheh Lit Chang

University of Washington

Problem 55

At what distance from a converging mirror with a $35 \mathrm{cm}$ focal length should an object be placed so that its image is the same distance from the mirror as the object?

Sheh Lit Chang

University of Washington

Problem 56

The sun is $150,000,000 \mathrm{km}$ from earth; its diameter is $1,400,000 \mathrm{km} .$ A student uses a $4.0-\mathrm{cm}-$ diameter lens with $f=10 \mathrm{cm}$ to cast an image of the sun on a piece of paper.
a. Where should the paper be placed to get a sharp image?
b. What is the diameter of the image on the paper?
c. The intensity of the incoming sunlight is $1050 \mathrm{W} / \mathrm{m}^{2} .$ What is the power of the light captured by the lens?
d. What is the intensity of sunlight in the projected image? Assume that all of the light captured by the lens is focused into the image.

Sheh Lit Chang

University of Washington

Problem 57

The illumination lights in an operating room use a converging mirror to focus an image of a bright lamp onto the surgical site. One such light has a mirror with a focal length of $15 \mathrm{cm} .$ If the patient is $1.0 \mathrm{m}$ from the mirror, where should the lamp be placed relative to the mirror?

Vishal Gupta

Numerade Educator

Problem 58

The sun is $150,000,000 \mathrm{km}$ from earth; its diameter is $1,400,000 \mathrm{km}$ For a science project on solar For a science project on solar power, a student uses a 24 -cm-diameter converging mirror with a focal length of $45 \mathrm{cm}$ to focus sunlight onto an object. This casts an image of the sun on the object. For the most intense heat, the image of the sun should be in focus.
a. Where should the object be placed?
b. What is the diameter of the image?
c. The intensity of the incoming sunlight is $1050 \mathrm{W} / \mathrm{m}^{2} .$ What is the total power of the light captured by the mirror?
d. What is the intensity of sunlight in the projected image? Assume that all of the light captured by the mirror is focused into the image.

Sheh Lit Chang

University of Washington

Problem 59

The moon is $3.5 \times 10^{6} \mathrm{m}$ in diameter and $3.8 \times 10^{8} \mathrm{m}$ from the earth's surface. The 1.2 -m-focal-length converging mirror of a telescope focuses an image of the moon onto a detector. What is the diameter of the moon's image?

Sheh Lit Chang

University of Washington

Problem 60

Consider a typical diverging passenger-side mirror with a focal length of $-80 \mathrm{cm} .$ A $1.5-\mathrm{m}$ -tall cyclist on a bicycle is $25 \mathrm{m}$ from the mirror. You are $1.0 \mathrm{m}$ from the mirror, and suppose, for simplicity, that the mirror, you, and the cyclist all lie along a line.
a. How far are you from the image of the cyclist?
b. What is the image height?

Sheh Lit Chang

University of Washington

Problem 61

You slowly back away from a plane mirror at a speed of $0.10 \mathrm{m} / \mathrm{s} .$ With what speed does your image appear to be moving away from you?

Sheh Lit Chang

University of Washington

Problem 62

At what angle $\phi$ should the laser beam in Figure $\mathrm{P} 18.62$ be aimed at the mirrored ceiling in order to hit the midpoint of the far wall?

Sheh Lit Chang

University of Washington

Problem 63

A laser beam is incident on a mirror at an angle of $30^{\circ},$ as shown in Figure $\mathrm{P} 18.63 .$ It reflects off the mirror and strikes a wall $2.0 \mathrm{m}$ away at point $\mathrm{P.By}$ what distance does the laser spot on the wall move if the mirror is rotated by $10^{\circ} ?$

Sheh Lit Chang

University of Washington

Problem 64

The place you get your hair cut has two nearly parallel mirrors $5.0 \mathrm{m}$ apart. As you sit in the chair, your head is $2.0 \mathrm{m}$ from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

Rodger Claar

Numerade Educator

Problem 65

What is the angle of incidence in air of a light ray whose angle of refraction in glass is half the angle of incidence?

Rodger Claar

Numerade Educator

Problem 66

Figure P18.66 shows a light ray incident on a glass cylinder. What is the angle $\alpha$ of the ray after it has entered the cylinder?

Sheh Lit Chang

University of Washington

Problem 67

It's nighttime, and you've dropped your goggles into a swimming pool that is $3.0 \mathrm{m}$ deep. If you hold a laser pointer $1.0 \mathrm{m}$ directly above the edge of the pool, you can illuminate the goggles if the laser beam enters the water $2.0 \mathrm{m}$ from the edge. How far are the goggles from the edge of the pool?

Sheh Lit Chang

University of Washington

Problem 68

Figure $\mathrm{P} 18.68 \quad$ shows $\quad \mathrm{a}$ meter stick lying on the bottom of a $100-\mathrm{cm}$ -long tank with its zero mark against the left edge. You look into the tank at a $30^{\circ}$ angle, with your line of sight just grazing the upper left
edge of the tank. What mark do you see on the meter stick if the tank is (a) empty, (b) half full of water, and (c) completely full of water?

Sheh Lit Chang

University of Washington

Problem 69

What is the exit angle $\theta$ from the glass prism in Figure $\mathrm{P} 18.69 ?$

Sheh Lit Chang

University of Washington

Problem 70

What is the smallest angle $\theta_{1}$ for which a laser beam will undergo total internal reflection on the hypotenuse of the glass prism in Figure $\mathrm{P} 18.70 ?$

Sheh Lit Chang

University of Washington

Problem 71

A 1.0-cm-thick layer of water stands on a horizontal slab of glass. Light from within the glass is incident on the glass-water boundary. What is the maximum angle of incidence for which a light ray can emerge into the air above the water?

Sheh Lit Chang

University of Washington

Problem 72

The glass core of an optical fiber has index of refraction 1.60. The index of refraction of the cladding is $1.48 .$ What is the maximum angle between a light ray and the wall of the core if the ray is to remain inside the core?

Sheh Lit Chang

University of Washington

Problem 73

A 150-cm-tall diver is standing completely submerged on the bottom of a swimming pool full of water. From your point of view out of the water, on the edge of the pool, how tall does the diver appear to be?

Sheh Lit Chang

University of Washington

Problem 74

To a fish, the $4.00-\mathrm{mm}$ -thick aquarium walls appear only $3.50 \mathrm{mm}$ thick. What is the index of refraction of the walls?

Willis James

Numerade Educator

Problem 75

A microscope is focused on an amoeba. When a $0.15-\mathrm{mm}-$ thick cover glass $(n=1.50)$ is placed over the amoeba, by how far must the microscope objective be moved to bring the organism back into focus? Must it be raised or lowered?

Sheh Lit Chang

University of Washington

Problem 76

You need to use a $24-\mathrm{cm}$ -focal-length lens to produce an inverted image twice the height of an object. At what distance from the object should the lens be placed?

Sheh Lit Chang

University of Washington

Problem 77

A nearsighted person might correct his vision by wearing diverging lenses with focal length $f=-50 \mathrm{cm} .$ When wearing his glasses, he looks not at actual objects but at the virtual images of those objects formed by his glasses. Suppose he looks at a 12 -cm-long pencil held vertically $2.0 \mathrm{m}$ from his glasses. Use ray tracing to determine the location and height of the image.

Sheh Lit Chang

University of Washington

Problem 78

A 1.5-cm-tall object is 90 $\mathrm{cm}$ in front of a diverging lens that has a $45 \mathrm{cm}$ focal length. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.

Sheh Lit Chang

University of Washington

Problem 79

A 2.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 32 cm. How many places can you put the lens to form a well-focused image of the candle flame on the wall? For each location, what are the height and orientation of the image?

Narayan Hari

Numerade Educator

Problem 80

A 2.0-cm-diameter spider is 2.0 m from a wall. Determine the focal length and position (measured from the wall) of a lens that will make a half-size image of the spider on the wall.

Vishal Gupta

Numerade Educator

Problem 81

Figure P18.81 shows a meter stick held lengthwise along the optical axis of a converging mirror. How long is the image of the meter stick?

Sheh Lit Chang

University of Washington

Problem 82

A slide projector needs to create a 98 -cm-high image of a 2.0-cm-tall slide. The screen is $300 \mathrm{cm}$ from the slide.
a. What focal length does the lens need? Assume that it is a thin lens.
b. How far should you place the lens from the slide?

Vishal Gupta

Numerade Educator

Problem 83

There is an interesting optical effect you have likely noticed while driving along a flat stretch of road on a sunny day. A small, distant dip in the road appears to be filled with water. You may even see the reflection of an oncoming car. But, as you get closer, you find no puddle of water after all; the shimmering surface vanishes, and you see nothing but empty road. It was only a mirage, the name for this phenomenon.
The mirage is due to the different index of refraction of hot and cool air. The actual bending
of the light rays that produces the mirage is subtle, but we can make a simple model as follows. When air is heated, its density
decreases and so does its index of refraction. Consequently, a pocket of hot air in a dip in a road has a lower index of refraction than the cooler air above it. Incident light rays with large angles of incidence (that is, nearly parallel to the road, as shown in Figure P18.83) experience total internal reflection. The mirage that you see is due to this reflection. As you get nearer, the angle goes below the critical angle and there is no more total internal reflection; the “water” disappears!
The pocket of hot air appears to be a pool of water because
A. Light reflects at the boundary between the hot and cool air.
B. Its density is close to that of water.
C. Light refracts at the boundary between the hot and cool air.
D. The hot air emits blue light that is the same color as the daytime sky.

Sheh Lit Chang

University of Washington

Problem 84

There is an interesting optical effect you have likely noticed while driving along a flat stretch of road on a sunny day. A small, distant dip in the road appears to be filled with water. You may even see the reflection of an oncoming car. But, as you get closer, you find no puddle of water after all; the shimmering surface vanishes, and you see nothing but empty road. It was only a mirage, the name for this phenomenon.
The mirage is due to the different index of refraction of hot and cool air. The actual bending
of the light rays that produces the mirage is subtle, but we can make a simple model as follows. When air is heated, its density
decreases and so does its index of refraction. Consequently, a pocket of hot air in a dip in a road has a lower index of refraction than the cooler air above it. Incident light rays with large angles of incidence (that is, nearly parallel to the road, as shown in Figure P18.83) experience total internal reflection. The mirage that you see is due to this reflection. As you get nearer, the angle goes below the critical angle and there is no more total internal reflection; the “water” disappears!
Which of these changes would allow you to get closer to the mirage before it vanishes?
A. Making the pocket of hot air nearer in temperature to the air above it
B. Looking for the mirage on a windy day, which mixes the air layers
C. Increasing the difference in temperature between the pocket of hot air and the air above it
D. Looking at it from a greater height above the ground

Sheh Lit Chang

University of Washington

Problem 85

There is an interesting optical effect you have likely noticed while driving along a flat stretch of road on a sunny day. A small, distant dip in the road appears to be filled with water. You may even see the reflection of an oncoming car. But, as you get closer, you find no puddle of water after all; the shimmering surface vanishes, and you see nothing but empty road. It was only a mirage, the name for this phenomenon.
The mirage is due to the different index of refraction of hot and cool air. The actual bending
of the light rays that produces the mirage is subtle, but we can make a simple model as follows. When air is heated, its density
decreases and so does its index of refraction. Consequently, a pocket of hot air in a dip in a road has a lower index of refraction than the cooler air above it. Incident light rays with large angles of incidence (that is, nearly parallel to the road, as shown in Figure P18.83) experience total internal reflection. The mirage that you see is due to this reflection. As you get nearer, the angle goes below the critical angle and there is no more total internal reflection; the “water” disappears!
If you could clearly see the image of an object that was reflected by a mirage, the image would appear
A. Magnified.
B. With up and down reversed.
C. Farther away than the object.
D. With right and left reversed.

Sheh Lit Chang

University of Washington