Holt Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 14

Light And Reflection - all with Video Answers

Educators

Chapter Questions

Problem 1

Which band of the dectromagnctic spectrum has
a. the lowest frequency?
b. the shortest wavelength?

Meghan Miholics

Meghan Miholics

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Problem 2

Which of the following dectromagnctic waves has the highest frequency?
a. radio
b. ultraviolet radiation
c. blue light
d. infrared radiation

Meghan Miholics

Meghan Miholics

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Problem 3

Why can light be used to measure distances accurately? What must be known in order to make distance measurements?

Matt Braby

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Problem 4

For the diagram in Figure $14-28,$ use Huygens' principle to show what the wave front at point $A$ will look like at point B. How would you represcnt this wave front in the ray approximation?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 5

What is the relationship between the actual brightness of a light source and its apparent brightness from where you see it?

Matt Braby

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Problem 6

Suppose an intelligent society capable of receiving and transmitting radio signals lives on a planet orbiting Procyon, a star 95 light-years away from Earth. If a signal were scht toward Procyon in 1999 what is the carliest year that Earth could expect to receive a return message? (Hint: A light-year is the distance a ray of light travels in one year.)

Jacob Adamczyk

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Problem 7

How fast do X rays travel in a vacuum?

Matt Braby

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Problem 8

Why do astronomers observing distant galaxies talk about looking backward in time?

Jacob Adamczyk

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Problem 9

Do the brightest stars that you see in the night shy necessarily give off more light than dimmer stars? Explain your answer.

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Meghan Miholics

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Problem 10

The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between $7.5 \times 10^{14} \mathrm{Hz}$ and $1.0 \times 10^{15} \mathrm{Hz}$. To what wavelengths do these frequencies correspond? (See Sample Problem 14A.)

Meghan Miholics

Meghan Miholics

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Problem 11

The brightest light detected from the star Antares has a frequency of about $3 \times 10^{14} \mathrm{Hz}$. What is the wavelength of this light? (See Sample Problem 14 A)

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 12

What is the wavelength for an FM radio signal if the number on the dial reads $99.5 \mathrm{MHz}$ (See Sample Problem 14A.)

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 13

What is the wavelength of a radar signal that has a frequency of $33 \mathrm{GHz}$ ? (See Sample Problem 14A.)

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 14

For each of the objects listed below, identify whether light is reflected diffusely or specularly.
a. a concrete driveway
b. an undisturbed pond
c. a polished silver tray
d. a sheet of paper
e. a mercury column in a thermometer

Jacob Adamczyk

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Problem 15

If you are stranded on an island, where would you align a mirror to use sunlight to signal a searching aircraft?

Matt Braby

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Problem 16

If you are standing $2 \mathrm{m}$ in front of a flat mirror, how far behind the mirror is your image? What is the magnification of the image? Where is the image's right side with respect to your right side?

Jacob Adamczyk

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Problem 17

When you shine a flashlight across a room, you sec the beam of light on the wall. Why do you not sec the light in the air?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 18

How can an object be a specular reflector for some electromagnetic waves yet be diffuse for others?

Jacob Adamczyk

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Problem 19

A flat mirror that is $0.85 \mathrm{m}$ tall is nailed to a wall so that its upper edge is $1.7 \mathrm{m}$ above the floor. Use the law of reflection and a ray diagram to determine if this mirror will show a person who is $1.7 \mathrm{m}$ tall his or her complete reflection.

Matt Braby

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Problem 20

Two flat mirrors make an angle of $90.0^{\circ}$ with cach other, as diagrammed in Figure $14-29 .$ An incoming ray makes an angle of $35^{\circ}$ with the normal of mirror
A. Use the law of reflection to determine the angle of reflection from mirror
$B$. What is unusual about the incoming and reflected rays of light for this arrangement of mirrors?

Meghan Miholics

Meghan Miholics

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Problem 21

If you walk $1.2 \mathrm{m} / \mathrm{s}$ toward a flat mirror, how fast does your image move? In what direction does your image move with respect to you?

Matt Braby

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Problem 22

Why do the images produced by two opposing flat mirrors appear to be progressively smaller?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 23

What type of mirror should be used to project movie images on a large screen?

Matt Braby

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Problem 24

If an object is placed outside the focal length of a concave mirror, what type of image will be formed? Will it appear in front of or behind the mirror?

Jacob Adamczyk

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Problem 25

Can you use a convex mirror to burn a hole in paper by focusing light rays at the mirror's focal point?

Matt Braby

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Problem 26

Can the image produced by a convex mirror ever be larger than the object?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 27

Why are parabolic mirrors preferred over spherical concave mirrors for use in reflecting telescopes?

Matt Braby

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Problem 28

Where does a ray of light that is parallel to the principal axis of a concave mirror go after it is reflected at the mirror's surface?

Jacob Adamczyk

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Problem 29

What happens to the real image produced by a concave mirror if you move the original object to the location of the image?

Matt Braby

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Problem 30

Consider a concave spherical mirror and a real object. Is the image always inverted? Is the image always real? Give conditions for your answers.

Jacob Adamczyk

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Problem 31

Explain why magnified images seem dimmer than the original objects.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 32

What test could you perform to determine if an image is real or virtual?

Jacob Adamczyk

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Problem 33

You've been given a concave mirror that may or may not be parabolic. What test could you perform to determine whether it is parabolic?

Matt Braby

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Problem 34

A concave shaving mirror has a radius of curvature of $25.0 \mathrm{cm} .$ For each of the following cases, find the magnification and determine whether the image formed is real or virtual and upright or inverted.
a. an upright pencil placed $45.0 \mathrm{cm}$ from the mirror
$\mathbf{b}$ an upright pencil placed $25.0 \mathrm{cm}$ from the mirror
c. an upright pencil placed $5.00 \mathrm{cm}$ from the mirror
(See Sample Problem 14B.)

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 35

A concave spherical mirror can be used to project an image onto a sheet of paper, allowing the magnified image of an illuminated real object to be accurately traced. If you have a concave mirror with a focal length of $8.5 \mathrm{cm},$ where would you place a sheet of paper so that the image projected onto it is twice as far from the mirror as the object is? Is the image upright or inverted, real or virtual? What would the magnification of the image be? (See Sample Problem $14 \mathrm{B}$.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 36

A convex mirror with a radius of curvature of $45.0 \mathrm{cm}$ forms a $1.70 \mathrm{cm}$ tall image of a pencil at a distance of $15.8 \mathrm{cm}$ behind the mirror. Calculate the object distance for the pencil and its height. Is the image real or virtual? What is the magnification? Is the image inverted or upright? (See Sample Problem 14C.)

Meghan Miholics

Meghan Miholics

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Problem 37

What are the three primary additive colors? What happens when you mix them?

Matt Braby

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Problem 38

What are the three primary subtractive colors (or primary pigments)? What happens when you mix them?

Jacob Adamczyk

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Problem 39

Explain why a polarizing disk used to analyze light can block light from a beam that has been passed through another polarizer. What is the relative orientation of the two polarizing disks?

Matt Braby

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Problem 40

Explain what could happen when you mix the following
a. cyan and yellow pigment
b. blue and yellow light
c. pure blue and pure yellow pigment
d. green and red light
e. pure green and pure blue pigment

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 41

What color would an opaque magenta shirt appear to be under the following colors of light?
a. white
b, red
c. cyan
d. green
e. yellow

Rashmi Sinha

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Problem 42

A substance is known to reflect green and blue light What color would it appear to be when it is illuminated by white light? by blue light?

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Problem 43

How can you tell if a pair of sunglasses has polarizing lenses?

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Problem 44

Why would sunglasses with polarizing lenses remove the glare from your view of the hood of your car or a distant body of water but not from a tall metal tank used for storing liquids?

Jacob Adamczyk

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Problem 45

Is light from the sky polarized? Why do clouds seen through Polaroid" glasses stand out in bold con. trast to the sky?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 46

The real image of a tree is magnified -0.085 times by a telescope's primary mirror. If the trec's image forms $35 \mathrm{cm}$ in front of the mirror, what is the distance between the mirror and the tree? What is the focal length of the mirror? What is the value for the mirror's radius of curvature? Is the image virtual or real? Is the image inverted or upright?

Ajay Singhal

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Problem 47

A candlestids holder has a concave reflector behind the candle, as shown in Figure $14-30 .$ The reflector magnifies a candle -0.75 times and forms an image $4.6 \mathrm{cm}$ away from the reflector's surface. Is the image inverted or upright? What are the object distance and the reflector's focal length? Is the image virtual or real?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

A child holds a candy bar $15.5 \mathrm{cm}$ in front of the convex side-view mirror of an automobile. The image height is reduced by one-half. What is the radius of curvature of the mirror?

Jacob Adamczyk

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Problem 49

A glowing electric light bulb placed $15 \mathrm{cm}$ from a concave spherical mirror produces a real image $8.5 \mathrm{cm}$ from the mirror. If the light bulb is moved to a position $25 \mathrm{cm}$ from the mirror, what is the position of the image? Is the final image real or virtual? What are the magnifications of the first and final images? Are the two images inverted or upright?

Matt Braby

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Problem 50

A convex mirror is placed on the ceiling at the intersection of two hallways. If a young man stands direct. ly underneath the mirror, his shoe, which is a distance of $195 \mathrm{cm}$ from the mirror, forms an image that appears $12.8 \mathrm{cm}$ behind the mirror's surface. What is the mirror's focal length? What is the magnification of the image? Is the image real or virtual Is the image upright or inverted?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 51

The side-view mirror of an automobile has a radius of curvature of $11.3 \mathrm{cm} .$ The mirror produces a virtwal image one-third the size of the object. How far is the object from the mirror?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

An object is placed $10.0 \mathrm{cm}$ in front of a mirror. What type must the mirror be to form an image of the object on a wall $2.00 \mathrm{m}$ away from the mirror? What is the magnification of the image? Is the image real or virtual? Is the image inverted or upright?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

The reflecting surfaces of two intersecting flat mirrors are at an angle of $\theta\left(0^{\circ}<\theta<90^{\circ}\right),$ as shown in Figure $14-31 .$ A light ray strikes the horizontal mirror. Use the law of reflection to show that the emerg. ing ray will intersect the incident ray at an angle of $\phi=180^{\circ}-2 \theta$.

Matt Braby

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Problem 54

Show that if a flat mirror is assumed to have an "infinite" radius of curvature, the mirror equation reduces to $q=-p$.

Jacob Adamczyk

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Problem 55

A real object is placed at the zero end of a meterstick. A large concave mirror at the $100.0 \mathrm{cm}$ end of the meterstick forms an image of the object at the $70.0 \mathrm{cm}$ position. A small convex mirror placed at the $20.0 \mathrm{cm}$ position forms a final image at the $10.0 \mathrm{cm}$ point. What is the radius of curvature of the convex mirror?

Meghan Miholics

Meghan Miholics

Numerade Educator

Problem 56

A dedicated sports-car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face $30.0 \mathrm{cm}$ behind the hubcap. He then turns the hubcap over and sees another image of his face $10.0 \mathrm{cm}$ behind the hubcap.
a. How far is his face from the hubcap?
b. What is the radius of curvature of the hubcap?
c. What is the magnification for each image?
d. Are the images real or virtual?
e. Are the images upright or inverted?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 57

An object $2.70 \mathrm{cm}$ tall is placed $12.0 \mathrm{cm}$ in front of a mirror. What type of mirror and what radius of curvature are needed to create an upright image that is $5.40 \mathrm{cm}$ in height? What is the magnification of the image? Is the image real or virtual?

Matt Braby

Numerade Educator

Problem 58

A "floating coin" illusion consists of two parabolic mirrors, each with a focal length of $7.5 \mathrm{cm},$ facing each other so that their centers are $7.5 \mathrm{cm}$ apart (see Figure $14-32$ ). If a few coins are placed on the lower mirror, an image of the coins forms in the small opening at the center of the top mirror. Use the mirror equation and draw a ray diagram to show that the final image forms at that location. Show that the magnification is 1 and that the image is real and upright. (Note: A flashlight beam shone on these images has a very startling effect. Even at a glancing angle, the incoming light beam is seemingly reflected off the images of the coins. Do you understand why?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

Use the mirror equation and the cquation for mag. nification to prove that the image of a real object formed by a convex mirror is always upright, virtual, and smaller than the object. Use the same equations to prove that the image of a real object placed in front of any spherical mirror is always virtual and upright when $p< $ l f l.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 60

Use trigonometry to derive the mirror and magnification equations from the ray diagram in Figure 14-11 on page 531. (Hint: Note that the incoming ray between the light-bulb filament and the mirror forms the hypotenuse of a right triangle. The reflected ray between the image point and the mirror is also the hypotenuse of a right triangle.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator