Physics: Principles with Applications

Douglas C. Giancoli

Chapter 23

LIGHT: GEOMETRIC OPTICS - all with Video Answers

Educators

Chapter Questions

Problem 1

(I) When you look at yourself in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

Zachary Warner

Zachary Warner

Numerade Educator

Problem 2

(I) Suppose that you want to take a photograph of yourself as you look at your image in a mirror 3.1 m away. For what distance should the camera lens be focused?

Kyle Godbey

Numerade Educator

Problem 3

(II) Two plane mirrors meet at a 135$^\circ$ angle, Fig. 23-52. If light rays strike one mirror at 34$^
circ as shown, at what angle $\phi$ do they leave the second mirror?
FIGURE 23–52 Problem 3. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 4

(II) A person whose eyes are 1.72 m above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor, Fig. 23-53. What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor an be seen reflected in the mirror?
FIGURE 23–53 Problem 4. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 5

(II) Stand up two plane mirrors so they form a 90.0$^\circ$ angle as in Fig. 23-54. When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a
ray diagram to show how this occurs.
FIGURE 23–54 Problem 5. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 6

(II) Two plane mirrors, nearly parallel, are facing each other 2.3 m apart as in Fig. 23-55. You stand 1.6 m away from one of these mirrors and look into it. You will see multiple images of yourself. (a) How far away from you are the first three images of yourself in the mirror in front of you? (b) Are these first three images facing toward you or away from you?
FIGURE 23–55 Problem 6. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 7

(III) Suppose you are 94 cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye rom a point on the tip of your nose if your pupil diameter is 4.5 mm?

Zachary Warner

Numerade Educator

Problem 8

(I) A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun's rays 18.8 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?

Kyle Godbey

Numerade Educator

Problem 9

(I) How far from a concave mirror (radius 21.0 cm) must an object be placed if its image is to be at infinity?

Zachary Warner

Numerade Educator

Problem 10

(II) A small candle is 38 cm from a concave mirror having a radius of curvature of 24 cm. (a) What is the focal length of the mirror? (b) Where will the image of the candle be located? (c) Will the image be upright or inverted?

Kyle Godbey

Numerade Educator

Problem 11

(II) An object 3.0 mm high is placed 16 cm from a convex mirror of radius of curvature 16 cm. (a) Show by ray tracing that the image is virtual, and estimate the image distance. (b) Show that the (negative) image distance can be computed from Eq. 23-2 using a focal length of (c) Compute
the image size, using Eq. 23-3.

Zachary Warner

Numerade Educator

Problem 12

(II) A dentist wants a small mirror that, when 2.00 cm from a tooth, will produce a upright image. What kind of mirror must be used and what must its radius of curvature be?

Kyle Godbey

Numerade Educator

Problem 13

(II) You are standing 3.4 m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror.

Zachary Warner

Numerade Educator

Problem 14

(II) The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 19.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?

Kyle Godbey

Numerade Educator

Problem 15

(II) A mirror at an amusement park shows an upright image of any person who stands 1.9 m in front of it. If the image is three times the person's height, what is the radius of curvature of the mirror? (See Fig. 23-50.)

Zachary Warner

Numerade Educator

Problem 16

(II) In Example 23-4, show that if the object is moved 10.0 cm farther from the concave mirror, the object's image size will equal the object's actual size. Stated as a multiple of the focal length, what is the object distance for this "actual-sized image" situation?

Kyle Godbey

Numerade Educator

Problem 17

(II) You look at yourself in a shiny 8.8-cm-diameter Christmas tree ball. If your face is 25.0 cm away from the ball's front surface, where is your image? Is it real or virtual? Is it upright or inverted?

Zachary Warner

Numerade Educator

Problem 18

(II) Some rear view mirrors produce images of cars to your rear that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror's radius of curvature if cars 16.0 m away appear 0.33 their normal size?

Kyle Godbey

Numerade Educator

Problem 19

(II) When walking toward a concave mirror you notice that the image flips at a distance of 0.50 m. What is the radius of curvature of the mirror?

Zachary Warner

Numerade Educator

Problem 20

(II) (a) Where should an object be placed in front of a concave mirror so that it produces an image at the same location as the object? (b) Is the image real or virtual? (c) Is the image inverted or upright? (d) What is the magnification of the image?

Kyle Godbey

Numerade Educator

Problem 21

(II) A shaving or makeup mirror is designed to magnify your face by a factor of 1.40 when your face is placed 20.0 cm in front of it. (a) What type of mirror is it? (b) Describe the type of image that it makes of your face. (c) Calculate the required radius of curvature for the mirror.

Vishal Gupta

Numerade Educator

Problem 22

(II) Use two techniques, (a) a ray diagram, and (b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C(d_o >r) $, and is greater than 1 if the object is within $C(d_o < r) $.

Kyle Godbey

Numerade Educator

Problem 23

(III) Show, using a ray diagram, that the magnification m of a convex mirror $m= -d_i/d_o$,is just as for a concave mirror. $[Hint$: Consider a ray from the top of the object that reflects at the center of the mirror.]

Zachary Warner

Numerade Educator

Problem 24

(III) An object is placed a distance r in front of a wall, where r exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? What is the magnification of the image?

Kyle Godbey

Numerade Educator

Problem 25

(I) The speed of light in ice is What is $2.29\times 10^8m/s$ the index of refraction of ice?

Zachary Warner

Numerade Educator

Problem 26

(I) What is the speed of light in (a) ethyl alcohol, (b) lucite, (c) crown glass?

Kyle Godbey

Numerade Educator

Problem 27

(II) The speed of light in a certain substance is 82% of its value in water. What is the index of refraction of that substance?

Zachary Warner

Numerade Educator

Problem 28

(I) A flashlight beam strikes the surface of a pane of glass $(n=1.56)$ at a 67$^\circ$ angle to the normal. What is the angle of refraction?

Kyle Godbey

Numerade Educator

Problem 29

(I) A diver shines a flashlight upward from beneath the water at a 35.2$^\circ$ angle to the vertical. At what angle does the light leave the water?

Zachary Warner

Numerade Educator

Problem 30

(I) A light beam coming from an underwater spotlight exits the water at an angle of 56.0$^\circ$. At what angle of incidence did it hit the air water interface from below the surface?

Kyle Godbey

Numerade Educator

Problem 31

(I) Rays of the Sun are seen to make a 36.0$^\circ$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?

Zachary Warner

Numerade Educator

Problem 32

(II) An aquarium filled with water has flat glass sides whose index of refraction is 1.54. A beam of light from outside the aquarium strikes the glass at a 43.5$^\circ$ angle to the perpendicular (Fig. 23-56). What is the angle of this light ray when it enters (a) the glass, and then (b) the water? (c) What would be the refracted angle if the ray entered the water directly?
FIGURE 23–56 Problem 32. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 33

(II) A beam of light in air strikes a slab of glass and is partially reflected and partially refracted. Determine the angle of incidence if the angle of reflection is twice the angle of refraction.

Zachary Warner

Numerade Educator

Problem 34

(II) In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.5 m from his foot at the edge of the pool (Fig. 23-57). Where does the spot of light hit the bottom of the 2.1-m-deep pool? Measure from the bottom of the wall beneath his foot.
FIGURE 23–57 Problem 34. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 35

(I) What is the critical angle for the interface between water and crown glass? To be internally reflected, the light must start in which material?

Supratim Pal

Numerade Educator

Problem 36

(I) The critical angle for a certain liquid-air surface is 47.2$^\circ$. What is the index of refraction of the liquid?

Kyle Godbey

Numerade Educator

Problem 37

(II) A beam of light is emitted in a pool of water from a depth of 82.0 cm. Where must it strike the air-water interface, relative to the spot directly above it, in order that the light does $not$ exit the water?

Zachary Warner

Numerade Educator

Problem 38

(II) A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes the air surface 7.6 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid?

Kyle Godbey

Numerade Educator

Problem 39

(III) (a) What is the minimum index of refraction for a glass or plastic prism to be used in binoculars (Fig. 23-28) so that total internal reflection occurs at 45$^\circ$ ? (b) Will binoculars work if their prisms (assume n= 1.58) are immersed in water? (c) What minimum n is needed if the prisms are immersed in water?

Zachary Warner

Numerade Educator

Problem 40

(III) A beam of light enters the end of an optic fiber as shown in Fig. 23-58. (a) Show that we can guarantee total internal reflection at the side surface of the material (at point A), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point A, assuming air outside. (b) What if the fiber were immersed in water?
FIGURE 23–58 Problem 40. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 41

(I) A sharp image is located 391 mm behind a 215-mm- focal-length converging lens. Find the object distance (a) using a ray diagram, (b) by calculation.

Zachary Warner

Numerade Educator

Problem 42

(I) Sunlight is observed to focus at a point 16.5 cm behind a lens. (a) What kind of lens is it? (b) What is its power in diopters?

Kyle Godbey

Numerade Educator

Problem 43

(I) (a) What is the power of a 32.5-cm-focal-length lens? (b) What is the focal length of a lens? Are these
lenses converging or diverging?

Zachary Warner

Numerade Educator

Problem 44

(II) A certain lens focuses light from an object 1.55 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?

Kyle Godbey

Numerade Educator

Problem 45

(II) A 105-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 132 mm. (a) How far in front of the sensor should the lens (assumed thin) be positioned if the object to be photographed is 10.0 m away? (b) 3.0 m away? (c) 1.0 m away? (d) What is the closest object this lens could photograph sharply?

Zachary Warner

Numerade Educator

Problem 46

(II) Use ray diagrams to show that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is real.

Kyle Godbey

Numerade Educator

Problem 47

(II) Use ray diagrams to show that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is real.

Zachary Warner

Numerade Educator

Problem 48

(II) It is desired to magnify reading material by a factor of $3.0\times$ when a book is placed 9.0 cm behind a lens. (a) Draw a ray diagram and describe the type of image this would be. (b) What type of lens is needed? (c) What is the power of the lens in diopters?

Kyle Godbey

Numerade Educator

Problem 49

(II) A-7.00-D lens is held 12.5 cm from an ant 1.00 mm high. Describe the position, type, and height of the image.

Zachary Warner

Numerade Educator

Problem 50

(II) An object is located 1.50 m from a 6.5-D lens. By how much does the image move if the object is moved (a) 0.90 m closer to the lens, and (b) 0.90 m farther from the lens?

Kyle Godbey

Numerade Educator

Problem 51

(II) (a) How far from a 50.0-mm-focal-length lens must an object be placed if its image is to be magnified and be real? (b) What if the image is to be virtual and magni-fied 2.50X?

Zachary Warner

Numerade Educator

Problem 52

(II) Repeat Problem 51 for a lens. $[Hint$: Consider objects real or virtual (formed by some
other piece of optics).]

Kyle Godbey

Numerade Educator

Problem 53

(II) How far from a converging lens with a focal length of 32 cm should an object be placed to produce a real image which is the same size as the object?

Zachary Warner

Numerade Educator

Problem 54

(II) (a) A 2.40-cm-high insect is 1.30 m from a 135-mm- focal-length lens. Where is the image, how high is it, and what type is it? (b) What if $f = 135 mm$?

Kyle Godbey

Numerade Educator

Problem 55

(III) A bright object and a viewing screen are separated by a distance of 86.0 cm. At what location(s) between the object and the screen should a lens of focal length 16.0 cm be placed in order to produce a sharp image on the screen? [$Hint$: First draw a diagram.]

Zachary Warner

Numerade Educator

Problem 56

(III) How far apart are an object and an image formed by an 85-cm-focal-length converging lens if the image is 3.25 X larger than the object and is real?

Kyle Godbey

Numerade Educator

Problem 57

(III) In a film projector, the film acts as the object whose image is projected on a screen (Fig. 23-59). If a 105-mm-focal-length lens is to project an image on a screen 25.5 m away, how far from the lens should the film be? If the film is 24 mm wide, how wide will the picture be on the screen?
FIGURE 23–59 Film projector, Problem 57 (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 58

(II) A diverging lens with $f = -36.5 cm$ is placed 14.0 cm behind a converging lens with $ f = 20.0 cm. Where will an object at infinity be focused?

Kyle Godbey

Numerade Educator

Problem 59

(II) Two 25.0-cm-focal-length converging lenses are placed 16.5 cm apart. An object is placed 35.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnification?

Zachary Warner

Numerade Educator

Problem 60

(II) A 38.0-cm-focal-length converging lens is 28.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: First draw a ray diagram.]

Kyle Godbey

Numerade Educator

Problem 61

(II) Two lenses, one converging with focal length 20.0 cm and one diverging with focal length -10.0 cm, are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine ($a$) the position and ($b$) the magnification of the final image formed. ($c$) Sketch a ray diagram for this system.

Zachary Warner

Numerade Educator

Problem 62

(II) A lighted candle is placed 36 cm in front of a converging lens of focal length $f_1= 13 cm,$ which in turn is 56 cm in front of another converging lens of focal length $f_2=16 cm$ (see Fig. 23-60). (a) Draw a ray diagram and estimate the location and the relative size of the final image. (b) Calculate the position and relative size of the final image.
FIGURE 23–60 Problem 62. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 63

(I) A double concave lens has surface radii of 33.4 cm and 28.8 cm. What is the focal length if n = 1.52?

Zachary Warner

Numerade Educator

Problem 64

(I) Both surfaces of a double convex lens have radii of 34.1 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens material?

Kyle Godbey

Numerade Educator

Problem 65

(I) A planoconvex lens (Fig. 23-31a) with n = 1.55 is to have a focal length of 16.3 cm. What is the radius of curvature of the convex surface?

Zachary Warner

Numerade Educator

Problem 66

(II) A symmetric double convex lens with a focal length of 22.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface?

Kyle Godbey

Numerade Educator

Problem 67

(II) A prescription for an eyeglass lens calls for +3.50 diopters. The lensmaker grinds the lens from a "blank" with n = 1.56 and convex front surface of radius of curvature of 30.0 cm. What should be the radius of curvature of the other surface?

Zachary Warner

Numerade Educator

Problem 68

(III) An object is placed 96.5 cm from a glass lens with one concave surface of radius 22.0 cm and one convex surface of radius 18.5 cm. Where is the final image? What is the magnification?

Kyle Godbey

Numerade Educator

Problem 69

Sunlight is reflected off the Moon. How long does it take that light to reach us from the Moon?

Zachary Warner

Numerade Educator

Problem 70

You hold a small flat mirror 0.50 m in front of you and can see your reflection twice in that mirror because there is a full-length mirror 1.0 m behind you (Fig. 23-61). Determine the distance of
each image from you.
FIGURE 23–61 Problem 70. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 71

We wish to determine the depth of a swimming pool filled with water by measuring the width (x = 6.50 m) and then noting that the far bottom edge of the pool is just visible at an angle of 13.0$^\circ$ above the horizontal as shown in Fig. 23-62. Calculate the depth of the pool.
FIGURE 23–61 Problem 70. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 72

The critical angle of a certain piece of plastic in air is $\theta_C$ = 37.8$^\circ$. What is the critical angle of the same plastic if it is immersed in water?

Kyle Godbey

Numerade Educator

Problem 73

A pulse of light takes 2.63 ns (see Table 1-4) to travel 0.500 m in a certain material. Determine the material's index of refraction, and identify this material.

Zachary Warner

Numerade Educator

Problem 74

When an object is placed 60.0 cm from a certain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.

Kyle Godbey

Numerade Educator

Problem 75

A 4.5-cm-tall object is placed 32 cm in front of a spherical mirror. It is desired to produce a virtual image that is upright and 3.5 cm tall. ($a$) What type of mirror should be used? ($b$) Where is the image located? ($c$) What is the focal length of the mirror? ($d$) What is the radius of curvature of the mirror?

Zachary Warner

Numerade Educator

Problem 76

Light is emitted from an ordinary light bulb filament in wave-train bursts of about $10^{-8}$ s in duration. What is the length in space of such wave trains?

Kyle Godbey

Numerade Educator

Problem 77

If the apex angle of a prism is $\phi=75$ $^\circ$ (see Fig. 23-63), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given n = 1.58?
FIGURE 23–63 Problem 77. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 78

($a$) A plane mirror can be considered a limiting case of a spherical mirror. Specify what this limit is. ($b$) Determine an equation that relates the image and object distances in this limit of a plane mirror. ($c$) Determine the magnification of a plane mirror in this same limit. ($d$) Are your results in parts ($b$) and ($c$) consistent with the discussion of Section 23-2 on plane mirrors?

Kyle Godbey

Numerade Educator

Problem 79

An object is placed 18 cm from a certain mirror. The image is half the height of the object, inverted, and real. How far is the image from the mirror, and what is the radius of curvature of the mirror?

Zachary Warner

Numerade Educator

Problem 80

Light is incident on an equilateral glass prism at a 45.0$^\circ$ angle to one face, Fig. 23-64. Calculate the angle at which light emerges from the opposite face. Assume that $n = 1.54$.
FIGURE 23–64 Problems 80 and 81. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 81

Suppose a ray strikes the left face of the prism in Fig. 23-64 at 45.0$^\circ$ as shown, but is totally internally reflected at the opposite side. If the apex angle (at the top) is $\theta=65.0^\circ$ what can you say about the index of refraction of the prism?
FIGURE 23–64 Problems 80 and 81. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 82

($a$) An object 37.5 cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtual? ($b$) If the image were located, instead, 44.5 cm in front of the lens, what type of lens would it be and what focal length would it have?

Kyle Godbey

Numerade Educator

Problem 83

How large is the image of the Sun on a camera sensor with ($a$) a 35-mm-focal-length lens, ($b$) a 50-mm-focal-length lens, and (c) a 105-mm-focal-length lens? The Sun has diameter $1.4\times10^6 km$ and it is $1.5\times10^8$ away.

Prabhu Ramji

Numerade Educator

Problem 84

Figure 23-65 is a photograph of an eyeball with the image of a boy in a doorway. ($a$) Is the eye here acting as a lens or as a mirror? ($b$) Is the eye being viewed right side up or is the camera taking this photo upside down? ($c$) Explain, based on all possible images made by a convex mirror or lens.
FIGURE 23–65 Problem 84. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 85

Which of the two lenses shown in Fig. 23-66 is converging, and which is diverging? Explain using ray diagrams and show how each image is formed.
FIGURE 23–66 Problem 85. (FIGURE CAN'T COPY)

Zachary Warner

Numerade Educator

Problem 86

Figure 23-67 shows a liquid-detecting prism device that might be used inside a washing machine. If no liquid covers the prism's hypotenuse, total internal reflection of the beam from the light source produces a large signal in the light sensor. If liquid covers the hypotenuse, some light escapes from the prism into the liquid and the light sensor's signal decreases. Thus a large signal from the light sensor indicates the absence of liquid in the reservoir. Determine the allowable range for the prism's index of refraction n.
FIGURE 23–67 Problem 86. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator

Problem 87

(a) Show that if two thin lenses of focal lengths $f_1$ and $f_2$ are placed in contact with each other, the focal length of the combination is given by $f_r-f_1f_2(f_1+f_2)$. (b) Show that the power $P$ of the combination of two lenses is the sum of their separate powers, $P=P_1+P_2.$

Zachary Warner

Numerade Educator

Problem 88

Two converging lenses are placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?

Kyle Godbey

Numerade Educator

Problem 89

An object is placed 30.0 cm from a +5.0-D lens. A spherical mirror with focal length 25 cm is placed 75 cm behind the lens. Where is the final image? (Note that the mirror reflects light back through the lens.) Be sure to draw a diagram.

Zachary Warner

Numerade Educator

Problem 90

A small object is 25.0 cm from a diverging lens as shown in Fig. 23-68. A converging lens with a focal length of 12.0 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens?
FIGURE 23–68 Problem 90. (FIGURE CAN'T COPY)

Kyle Godbey

Numerade Educator