Physics

Robert Coleman Richardson; Betty McCarthy Richardson; Alan Giambattista

Chapter 22

Electromagnetic Waves - all with Video Answers

Educators

JG

Chapter Questions

Problem 1

An electric dipole antenna used to transmit radio waves is oriented vertically.
At a point due south of the transmitter, what is the direction of the wave's magnetic field?

Mayukh Banik

Mayukh Banik

Numerade Educator

Problem 2

An electric dipole antenna used to transmit radio waves is oriented vertically.
At a point due north of the transmitter, how should a second electric dipole antenna be oriented to serve as a receiver?

Manish Jain

Numerade Educator

Problem 3

An electric dipole antenna used to transmit radio waves is oriented vertically.
At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a a receiver?

Mayukh Banik

Numerade Educator

Problem 4

An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.
At a point due east of the transmitter, what is the direction of the wave's electric field?

Mayukh Banik

Numerade Educator

Problem 5

An electric dipole antenna used to transmit radio waves is oriented horizontally north-south.
At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?

Narayan Hari

Numerade Educator

Problem 6

What is the wavelength of the radio waves broadcast by an FM radio station with a frequency of 90.9 MHz?

Mayukh Banik

Numerade Educator

Problem 7

What is the frequency of the microwaves in a microwave oven? The wavelength is $12 \mathrm{cm}$.

Mayukh Banik

Numerade Educator

Problem 8

How long does it take sunlight to travel from the Sun to Earth?

Mayukh Banik

Numerade Educator

Problem 9

How long does it take light to travel from this text to your eyes? Assume a distance of $50.0 \mathrm{cm} .$

Mayukh Banik

Numerade Educator

Problem 10

How far does a beam of light travel in 1 ns?

Mayukh Banik

Numerade Educator

Problem 11

In order to study the structure of a crystalline solid, you want to illuminate it with EM radiation whose wave-
length is the same as the spacing of the atoms in the crystal $(0.20 \mathrm{nm}) .$ (a) What is the frequency of the EM radiation? (b) In what part of the EM spectrum (radio, visible, etc.) does it lie?

JG

Jonelle Guzman

Numerade Educator

Problem 12

The currents in household wiring and power lines alternate at a frequency of $60.0 \mathrm{Hz}$. (a) What is the wavelength of the EM waves emitted by the wiring?
(b) Compare this wavelength with Earth's radius. (c) In what part of the EM spectrum are these waves?

Mayukh Banik

Numerade Educator

Problem 13

In musical acoustics, a frequency ratio of 2: 1 is called an octave. Humans with extremely good hearing can hear sounds ranging from $20 \mathrm{Hz}$ to $20 \mathrm{kHz}$, which is approximately 10 octaves $\left(\right.$ since $\left.2^{10}=1024 \approx 1000\right)$
(a) Approximately how many octaves of visible light are humans able to perceive? (b) Approximately how many octaves wide is the microwave region?

Mayukh Banik

Numerade Educator

Problem 14

In the United States, the ac household current oscillates at a frequency of $60 \mathrm{Hz}$. In the time it takes for the current to make one oscillation, how far has the electromagnetic wave traveled from the current-carrying wire? This distance is the wavelength of a $60 \mathrm{Hz}$ EM wave. Compare this length with the distance from Boston to Los Angeles $(4200 \mathrm{km})$.

Mayukh Banik

Numerade Educator

Problem 15

You are watching a baseball game on television that is being broadcast from $4500 \mathrm{km}$ away. The batter hits the ball with a loud "crack" of the bat. A microphone is located $22 \mathrm{m}$ from the batter, and you are $2.0 \mathrm{m}$ from the television set. On a day when sound travels $343 \mathrm{m} / \mathrm{s}$ in air, what is the minimum time it takes for you to hear the crack of the bat after the batter hits the ball?

Narayan Hari

Numerade Educator

Problem 16

You and a friend are sitting in the outfield bleachers of a Major League Baseball park, $140 \mathrm{m}$ from home plate on a day when the temperature is $20^{\circ} \mathrm{C}$. Your friend is listening to the radio commentary with headphones while watching. The broadcast network has a microphone located $17 \mathrm{m}$ from home plate to pick up the sound as the bat hits the ball. This sound is transferred as an EM wave a distance of $75000 \mathrm{km}$ by satellite from the ball park to the radio. (a) When the batter hits a hard line drive, who will hear the "crack" of the bat first, you or your friend, and what is the shortest time interval between the bat hitting the ball and one of you hearing the sound?
(b) How much later does the other person hear the sound?

Mayukh Banik

Numerade Educator

Problem 17

The speed of light in topaz is $1.85 \times 10^{8} \mathrm{m} / \mathrm{s} .$ What is the index of refraction of topaz?

Mayukh Banik

Numerade Educator

Problem 18

What is the speed of light in a diamond that has an index of refraction of $2.4168 ?$

Mayukh Banik

Numerade Educator

Problem 19

When the NASA Rover Spirit successfully landed on Mars in January of $2004,$ Mars was $170.2 \times 10^{6} \mathrm{km}$ from Earth. Twenty-one days later, when the Rover Opportunity landed on Mars, Mars was $198.7 \times 10^{6} \mathrm{km}$ from Earth. (a) How long did it take for a one-way transmission to the scientists on Earth from Spirit on its landing day?
(b) How long did it take for scientists to communicate with Opportunity on its landing day?

Narayan Hari

Numerade Educator

Problem 20

The index of refraction of water is $1.33 .$ (a) What is the speed of light in water? (b) What is the wavelength in water of a light wave with a vacuum wavelength of $515 \mathrm{nm} ?$

Mayukh Banik

Numerade Educator

Problem 21

Light of wavelength $692 \mathrm{nm}$ in air passes into window glass with an index of refraction of 1.52 .
(a) What is the wavelength of the light inside the glass?
(b) What is the frequency of the light inside the glass?

Mayukh Banik

Numerade Educator

Problem 22

Light travels through tanks filled with various substances. The indices of refraction of the substances $n$ and the lengths of the tanks are given. Rank them in order of the time it takes light to traverse the tank, from greatest to smallest.
(a) $n=5 / 4,$ length $=1 \mathrm{m}$
(b) $n=1,$ length $=4 / 5 \mathrm{m}$
$;$ (c) $n=1,$ length $=1 \mathrm{m}$
(d) $n=3 / 2,$ length $=1 \mathrm{m} ;$ (e) $n=3 / 2,$ length $=5 / 4 \mathrm{m}$
(f) $n=3 / 2,$ length $=4 / 5 \mathrm{m}$

JG

Jonelle Guzman

Numerade Educator

Problem 23

On a cold, autumn day, Tuan is staring out of the window watching the leaves blow in the wind. One bright yellow leaf is reflecting light that has a predominant wavelength of $580 \mathrm{nm}$
(a) What is the frequency of this light? (b) If the window glass has an index of refraction of $1.50,$ what are the speed, wavelength, and frequency of this light as it passes through the window?

Narayan Hari

Numerade Educator

Problem 24

The electric field in a microwave traveling through air has amplitude $0.60 \mathrm{mV} / \mathrm{m}$ and frequency $30 \mathrm{GHz}$. Find the amplitude and frequency of the magnetic field.

Mayukh Banik

Numerade Educator

Problem 25

The magnetic field in a microwave traveling through vacuum has amplitude $4.00 \times 10^{-11} \mathrm{T}$ and frequency $120 \mathrm{GHz}$. Find the amplitude and frequency of the electric field.

Mayukh Banik

Numerade Educator

Problem 26

The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}$ and frequency $3.0 \mathrm{MHz}$
(a) Find the amplitude and frequency of the electric field.
(b) The wave is traveling in the $-y$ -direction. At $y=0$ and $t=0,$ the magnetic field is $1.5 \times 10^{-11} \mathrm{T}$ in the +z-direction. What are the magnitude and direction of the electric field at $y=0$ and $t=0 ?$

Mayukh Banik

Numerade Educator

Problem 27

The electric field in a radio wave traveling through vacuum has amplitude $2.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ and frequency $1.47 \mathrm{MHz}$
(a) Find the amplitude and frequency of the magnetic field.
(b) The wave is traveling in the $+x$ -direction. At $x=0$ and $t=0,$ the electric field is $1.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ in the $-y$ -direction. What are the magnitude and direction of the magnetic field at $x=0$ and $t=0 ?$

Mayukh Banik

Numerade Educator

Problem 28

The magnetic field of an EM wave is given by $B_{y}=B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,$ and $B_{z}=0$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.

Mayukh Banik

Numerade Educator

Problem 29

The electric field of an EM wave is given by $E_{z}=E_{\mathrm{m}} \sin (k y-\omega t+\pi / 6), E_{x}=0,$ and $E_{y}=0$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the magnetic field of this wave.

Mayukh Banik

Numerade Educator

Problem 30

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately $1400 \mathrm{W} / \mathrm{m}^{2}$. (a) What is the average energy density? (b) Find the rms values of the electric and magnetic fields.

Mayukh Banik

Numerade Educator

Problem 31

The cylindrical beam of a $10.0 \mathrm{mW}$ laser is $0.85 \mathrm{cm}$ in diameter. What is the rms value of the electric field?

Mayukh Banik

Numerade Educator

Problem 32

In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two photographic plates in his lab to light coming through several pinholes. The source of light is $1.8 \mathrm{m}$ from one photographic plate and the exposure time is $1.0 \mathrm{h}$. For how long should Matt expose a second plate located $4.7 \mathrm{m}$ from the source if the second plate is to have equal exposure (i.e., the same energy collected)?

Manish Jain

Numerade Educator

Problem 33

A $1.0 \mathrm{m}^{2}$ solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs $1.4 \mathrm{kJ}$ of energy every second. The satellite is located at $1.00 \mathrm{AU}$ from the Sun. (The Earth-Sun distance is approximately 1 AU.) How long would it take an identical panel that is also oriented perpendicular to the incoming radiation to absorb the same amount of energy, if it were on an interplanetary exploration vehicle 1.55 AU from the Sun?

Narayan Hari

Numerade Educator

Problem 34

Fernando detects the electric field from an isotropic source that is $22 \mathrm{km}$ away by tuning in an electric field with an rms amplitude of $55 \mathrm{mV} / \mathrm{m}$. What is the average power of the source?

Mayukh Banik

Numerade Educator

Problem 35

A certain star is 14 million light-years from Earth. The intensity of the light that reaches Earth from the star is $4 \times 10^{-21} \mathrm{W} / \mathrm{m}^{2} .$ At what rate does the star radiate EM energy?

Mayukh Banik

Numerade Educator

Problem 36

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately $1400 \mathrm{W} / \mathrm{m}^{2}$ (a) What is the total average power output of the Sun, assuming it to be an isotropic source?
(b) What is the intensity of sunlight incident on Mercury, which is $5.8 \times 10^{10} \mathrm{m}$ from the Sun?

Mayukh Banik

Numerade Educator

Problem 37

The radio telescope in Arecibo, Puerto Rico, has a diameter of $305 \mathrm{m} .$ It can detect radio waves from space with intensities as small as $10^{-26} \mathrm{W} / \mathrm{m}^{2}$.
(a) What is the average power incident on the telescope due to a wave at normal incidence with intensity $1.0 \times 10^{-26} \mathrm{W} / \mathrm{m}^{2} ?$
(b) What is the average power incident on Earth's surface?
(c) What are the rms electric and magnetic fields?

Mayukh Banik

Numerade Educator

Problem 38

Prove that, in an EM wave traveling in vacuum, the electric and magnetic energy densities are equal; that is, prove that
$$
\frac{1}{2} \epsilon_{0} E^{2}=\frac{1}{2 \mu_{0}} B^{2}
$$
at any point and at any instant of time.

Mayukh Banik

Numerade Educator

Problem 39

Randomly polarized light with intensity $I_{0}$ passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles $\theta_{1}$ and $\theta_{2}$, respectively, to the horizontal. Rank the intensities of the light transmitted through the second polarizer, from greatest to least.
(a) $\theta_{1}=0^{\circ}, \theta_{2}=30^{\circ}$
(b) $\theta_{1}=30^{\circ}, \theta_{2}=30^{\circ}$
(c) $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$
(d) $\theta_{1}=60^{\circ}$
$\theta_{2}=0^{\circ} ;$ (e) $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ}$.

Manish Jain

Numerade Educator

Problem 40

Horizontally polarized light with intensity $I_{0}$ passes through two ideal polarizers, one after the other. The transmission axes of the first and second polarizers are at angles $\theta_{1}$ and $\theta_{2}$, respectively, to the horizontal. Rank the intensities of the light transmitted through the second polarizer, from greatest to least.
(a) $\theta_{1}=0^{\circ}$
$\theta_{2}=30^{\circ} ;$ (b) $\theta_{1}=30^{\circ}, \theta_{2}=30^{\circ} ;$ (c) $\theta_{1}=0^{\circ}, \theta_{2}=90^{\circ}$
(d) $\theta_{1}=60^{\circ}, \theta_{2}=0^{\circ} ;$ (e) $\theta_{1}=30^{\circ}, \theta_{2}=60^{\circ}$.

Urvashi Arora

Numerade Educator

Problem 41

Unpolarized light passes through two ideal polarizers in turn with polarization axes at $45^{\circ}$ to each other. What is the fraction of the incident light intensity that is transmitted?

Narayan Hari

Numerade Educator

Problem 42

Light polarized in the $x$ -direction shines through two ideal polarizing sheets. The first sheet's transmission axis makes an angle $\theta$ with the $x$ -axis, and the transmission axis of the second is parallel to the $y$ -axis. (a) If the incident light has intensity $I_{0},$ what is the intensity of the light transmitted through the second sheet? (b) At what angle $\theta$ is the transmitted intensity maximum?

Narayan Hari

Numerade Educator

Problem 43

Unpolarized light is incident on a system of three ideal polarizers. The second polarizer is oriented at an angle of $30.0^{\circ}$ with respect to the first, and the third is oriented at an angle of $45.0^{\circ}$ with respect to the first. If the light that emerges from the system has an intensity of $23.0 \mathrm{W} / \mathrm{m}^{2},$ what is the intensity of the incident light?

Narayan Hari

Numerade Educator

Problem 44

Unpolarized light is incident on four ideal polarizing sheets with their transmission axes oriented as shown in the figure. What percentage of the initial light intensity is transmitted through this set of polarizers?

Narayan Hari

Numerade Educator

Problem 45

A polarized beam of light has intensity $I_{0} .$ We want to rotate the direction of polarization by $90.0^{\circ}$ using ideal polarizing sheets.
(a) Explain why we must use at least two sheets. (b) What is the transmitted intensity if we use two sheets, each of which rotates the direction of polarization by $45.0^{\circ} ?$ (c) What is the transmitted intensity if we use four sheets, each of which rotates the direction of polarization by $22.5^{\circ} ?$

Manish Jain

Numerade Educator

Problem 46

Certically polarized microwaves traveling into the page are directed at each of three metal plates (a, b, c) that have parallel slots cut in them.
(a) Which plate transmits microwaves best?
(b) Which plate reflects microwaves best? (c) If the intensity transmitted through the best transmitter is $I_{1},$ what is the intensity transmitted through the second-best transmitter?

Manish Jain

Numerade Educator

Problem 47

Two sheets of ideal polarizing material are placed with their transmission axes at right angles to each other. A third polarizing sheet is placed between them with its transmission axis at $45^{\circ}$ to the axes of the other two. (a) If unpolarized light of intensity $I_{0}$ is incident on the system, what is the intensity of the transmitted light? (b) What is the intensity of the transmitted light when the middle sheet is removed?

Urvashi Arora

Numerade Educator

Problem 48

Vertically polarized light with intensity $I_{0}$ is normally incident on an ideal polarizer. As the polarizer is rotated about a horizontal axis, the intensity $I$ of light transmitted through the polarizer varies with the orientation of the polarizer $(\theta),$ where $\theta=0$ corresponds to a vertical transmission axis. Sketch a graph of $I$ as a function of $\theta$ for one complete rotation of the polarizer $\left(0 \leq \theta \leq 360^{\circ}\right)$.

Manish Jain

Numerade Educator

Problem 49

Just after sunrise, you look north at the sky just above the horizon. Is the light you see polarized? If so, in what direction?

Mayukh Banik

Numerade Educator

Problem 50

Just after sunrise, you look straight up at the sky. Is the light you see polarized? If so, in what direction?

Mayukh Banik

Numerade Educator

Problem 51

If the speeder in Example 22.9 were going faster than the police car, how fast would it have to go so that the reflected microwaves produce the same number of beats second?

Narayan Hari

Numerade Educator

Problem 52

Light of wavelength $659.6 \mathrm{nm}$ is emitted by a star. The wavelength of this light as measured on Earth is $661.1 \mathrm{nm} .$ How fast is the star moving with respect to Earth? Is it moving toward Earth or away from it?

Mayukh Banik

Numerade Educator

Problem 53

A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .$ Light of wavelength $480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

Mayukh Banik

Numerade Educator

Problem 54

A spaceship traveling $12.3 \mathrm{km} / \mathrm{s}$ relative to Earth sends out an EM pulse with a wavelength of $850.00 \mathrm{nm}$ (as measured by the source). The pulse is reflected from another spaceship that is moving toward the first spaceship at a speed of $24.6 \mathrm{km} / \mathrm{s}$ relative to Earth. What will be the wavelength of the reflected pulse as measured by the first spaceship?

Narayan Hari

Numerade Educator

Problem 55

A police car's radar gun emits microwaves with a frequency of $f_{1}=7.50 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving toward the police car at $48.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The speeder's radar detector detects the microwave at a frequency $f_{2}$.
(a) Which is larger, $f_{1}$ or $f_{2} ?$
(b) Find the frequency difference $f_{2}-f_{1}$.

Mayukh Banik

Numerade Educator

Problem 56

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?

Mayukh Banik

Numerade Educator

Problem 57

How fast would you have to drive in order to see a red light as green? Take $\lambda=630 \mathrm{nm}$ for red and $\lambda=530 \mathrm{nm}$ for green.

Mayukh Banik

Numerade Educator

Problem 58

The solar panels on the roof of a house measure $4.0 \mathrm{m}$ by $6.0 \mathrm{m}$. Assume they convert $12 \%$ of the incident EM wave's energy to electric energy.
(a) What average power do the panels supply when the incident intensity is $1.0 \mathrm{kW} / \mathrm{m}^{2}$ and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is $0.80 \mathrm{kW} / \mathrm{m}^{2}$ and the light is incident at an angle of $60.0^{\circ}$ from the normal? (c) Take the average daytime power requirement of a house to be about $2 \mathrm{kW}$. How do your answers to
(a) and (b) compare? What are the implications for the use of solar panels?

Manish Jain

Numerade Educator

Problem 59

A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0$ GHz. The beam reflects from a speeding car, which is moving away at $43.0 \mathrm{m} / \mathrm{s}$ with respect to the police car. The frequency of the reflected microwave as observed by the police is $f_{2}$. (a) Which is larger, $f_{1}$ or $f_{2} ?$ (b) Find the frequency difference $f_{2}-f_{1}$ [Hint: There are two Doppler shifts. First think of the police as source and the speeder as observer. The speeding car "retransmits" a reflected wave at the same frequency at which it receives the incident wave. $.]$

Manish Jain

Numerade Educator

Problem 60

Suppose some astronauts have landed on Mars. When the astronauts ask a question of mission control personnel on Earth, what is the shortest possible time they have to wait for a response? The average distance from Mars to the Sun is $2.28 \times 10^{11} \mathrm{m}$.

Narayan Hari

Numerade Educator

Problem 61

An AM radio station broadcasts at $570 \mathrm{kHz}$. (a) What is the wavelength of the radio wave in air? (b) If a radio is tuned to this station and the inductance in the tuning circuit is $0.20 \mathrm{mH},$ what is the capacitance in the tuning circuit? (c) In the vicinity of the radio, the amplitude of the electric field is $0.80 \mathrm{V} / \mathrm{m}$. The radio uses a coil antenna of radius $1.6 \mathrm{cm}$ with 50 turns. What is the maximum emf induced in the antenna, assuming it is oriented for best reception? Assume that the fields are sinusoidal functions of time.

Mayukh Banik

Numerade Educator

Problem 62

Consider the three ideal polarizing filters shown in the figure. The angles listed indicate the direction of the transmission axis of each polarizer with respect to the vertical.
(a) If unpolarized light of intensity $I_{0}$ is incident from the left, what is the intensity of the light that exits the last polarizer? (b) If vertically polarized light of intensity $I_{0}$ is incident from the left, what is the intensity of the light that exits the last polarizer? (c) Can you remove one polarizer from this series of filters so that light incident from the left is not transmitted at all if unpolarized light is incident as in part
(a)? If so, which polarizer should you remove? Answer the same questions for vertically polarized incident light as in part (b). (d) If you can remove one polarizer to maximize the amount of light transmitted in part (a), which one should you remove? Answer the same question for part (b).

Manish Jain

Numerade Educator

Problem 63

Calculate the frequency of an EM wave with a wavelength the size of (a) the thickness of a piece of paper $(60 \mu \mathrm{m}),$ (b) a $91 \mathrm{m}$ long soccer field, (c) the diameter of Earth, and (d) the distance from Earth to the Sun.

Narayan Hari

Numerade Educator

Problem 64

The intensity of solar radiation that falls on a detector on Earth is $1.00 \mathrm{kW} / \mathrm{m}^{2} .$ The detector is a square that measures $5.00 \mathrm{m}$ on a side and the normal to its surface makes an angle of 30.0 with respect to the Sun's radiation. How long will it take for the detector to measure $420 \mathrm{kJ}$ of energy?

Mayukh Banik

Numerade Educator

Problem 65

Astronauts on the Moon communicated with mission control in Houston via EM waves. There was a noticeable time delay in the conversation due to the round-trip transit time for the EM waves between the Moon and
Earth. How long was the time delay?

Mayukh Banik

Numerade Educator

Problem 66

The antenna on a wireless router radiates microwaves at a frequency of $5.0 \mathrm{GHz}$. What is the maximum length of the antenna if it is not to exceed half of a wavelength?

Narayan Hari

Numerade Educator

Problem 67

Two identical television signals are sent between two cities that are $400.0 \mathrm{km}$ apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time, but the one traveling through air arrives $7.7 \times 10^{-4} \mathrm{s}$ before the one traveling through the glass fiber. What is the index of refraction of the glass fiber?

Mayukh Banik

Numerade Educator

Problem 68

A laser used in LASIK eye surgery produces 55 pulses per second. The wavelength is 193 nm (in air), and each pulse lasts 10.0 ps. The average power emitted by the laser is $120.0 \mathrm{mW}$ and the beam diameter is $0.80 \mathrm{mm}$.
(a) In what part of the EM spectrum is the laser pulse? (b) How long (in centimeters) is a single pulse of the laser in air? (c) How many wavelengths fit in one pulse?

Manish Jain

Numerade Educator

Problem 69

A laser used in LASIK eye surgery produces 55 pulses per second. The wavelength is 193 nm (in air), and each pulse lasts 10.0 ps. The average power emitted by the laser is $120.0 \mathrm{mW}$ and the beam diameter is $0.80 \mathrm{mm}$.
(a) What is the total energy of a single pulse?
(b) What is the intensity during a pulse?

Manish Jain

Numerade Educator

Problem 70

A $2.0 \mathrm{mW}$ laser pointer has a beam diameter of $1.5 \mathrm{mm} .$ When it is accidentally pointed at a person's eye, the beam is focused to a spot of diameter $20.0 \mu \mathrm{m}$ on the retina and the retina is exposed for $80 \mathrm{ms}$. (a) What is the intensity of the laser beam?
(b) What is the intensity of light incident on the retina?
(c) What is the total energy incident on the retina?

Manish Jain

Numerade Educator

Problem 71

The range of wavelengths allotted to the radio broadcast band is from about $190 \mathrm{m}$ to $550 \mathrm{m}$. If each station needs exclusive use of a frequency band $10 \mathrm{kHz}$ wide, how many stations can operate in the broadcast band?

Mayukh Banik

Numerade Educator

Problem 72

Polarized light of intensity $I_{0}$ is incident on a pair of ideal polarizing sheets. Let $\theta_{1}$ and $\theta_{2}$ be the angles between the direction of polarization of the incident light and the transmission axes of the first and second sheets, respectively. Show that the intensity of the transmitted light is $I=I_{0} \cos ^{2} \theta_{1} \cos ^{2}\left(\theta_{1}-\theta_{2}\right)$.

Manish Jain

Numerade Educator

Problem 73

An unpolarized beam of light (intensity $I_{0}$ ) is moving in the $x$ -direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles $0.0^{\circ}, 45.0^{\circ},$ and $30.0^{\circ}$ counterclockwise from the $y$ -axis in the $y z$ -plane. (a) What is the intensity and polarization of the light that is transmitted by the last polarizer? (b) If the polarizer in the middle is removed, what is the intensity and polarization of the light transmitted by the last polarizer?

Mayukh Banik

Numerade Educator

Problem 74

A sinusoidal EM wave has an electric field amplitude $E_{\mathrm{m}}=32.0 \mathrm{mV} / \mathrm{m} .$ What are the intensity and average energy density? [Hint: Recall the relationship between amplitude and rms value for a quantity that varies sinusoidally.]

Mayukh Banik

Numerade Educator

Problem 75

Energy carried by an EM wave coming through the air can be used to light a bulb that is not connected to a battery or plugged into an electric outlet. Suppose a receiving antenna is attached to a bulb and the bulb is found to dissipate a maximum power of $1.05 \mathrm{W}$ when the antenna is aligned with the electric field coming from a distant source. The wavelength of the source is large compared to the antenna length. When the antenna is rotated so it makes an angle of $20.0^{\circ}$ with the incoming electric field, what is the power dissipated by the bulb?

Mayukh Banik

Numerade Educator

Problem 76

A $10 \mathrm{W}$ laser emits a beam of light $4.0 \mathrm{mm}$ in diameter. The laser is aimed at the Moon. By the time it reaches the Moon, the beam has spread out to a diameter of $85 \mathrm{km} .$ Ignoring absorption by the atmosphere, what is the intensity of the light (a) just outside the laser and
(b) where it hits the surface of the Moon?

Mayukh Banik

Numerade Educator

Problem 77

You are trying to communicate with a spaceship that is traveling at $1.2 \times 10^{8} \mathrm{m} / \mathrm{s}$ away from Earth. If you send a message at a frequency of $55 \mathrm{kHz}$, to what frequency should the astronauts on the ship tune to receive your message?

Manish Jain

Numerade Educator

Problem 78

To measure the speed of light, Galileo and a colleague stood on different mountains with covered lanterns. Galileo uncovered his lantern and his friend, seeing the light, uncovered his own lantern in turn. Galileo measured the elapsed time from uncovering his lantern to seeing the light signal response. The elapsed time should be the time for the light to make the round trip plus the reaction time for his colleague to respond. To determine reaction time, Galileo repeated the experiment while he and his friend were close to one another. He found the same time whether his colleague was nearby or far away and concluded that light traveled almost instantaneously. Suppose the reaction time of Galileo's colleague was $0.25 \mathrm{s}$ and for Galileo to observe a difference, the complete round trip would have to take 0.35 s. How far apart would the two mountains have to be for Galileo to observe a finite speed of light? Is this feasible?

Mayukh Banik

Numerade Educator

Problem 79

What are the three lowest angular speeds for which the wheel in Fizeau's apparatus (see Fig. 22.11 ) allows the reflected light to pass through to the observer? Assume the distance between the notched wheel and the mirror
is $8.6 \mathrm{km}$ and that there are 5 notches in the wheel.

Mayukh Banik

Numerade Educator

Problem 80

By expressing $\epsilon_{0}$ and $\mu_{0}$ in base SI units (kg, $m,$ s, A), show that the only combination of the two with dimensions of speed is $\left(\epsilon_{0} \mu_{0}\right)^{-1 / 2}$.

Urvashi Arora

Numerade Educator

Problem 81

A microwave oven can heat $350 \mathrm{g}$ of water from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{Cin} 2.00 \mathrm{min} .$ (a) At what rate is energy absorbed by the water? (b) These microwaves pass through a waveguide of cross-sectional area $88.0 \mathrm{cm}^{2} .$ What is the average intensity of the microwaves in the waveguide? (c) What are the rms electric and magnetic fields inside the waveguide?

Manish Jain

Numerade Educator

Problem 82

Verify that the equation $I=\langle u\rangle c$ is dimensionally consistent (i.e., check the units).

Mayukh Banik

Numerade Educator

Problem 83

Using Faraday's law, show that if a magnetic dipole antenna's axis makes an angle $\theta$ with the magnetic field of an EM wave, the induced emf in the antenna is reduced from its maximum possible value by a factor of cos $\theta$. [ Hint: Assume that, at any instant, the magnetic field everywhere inside the loop is uniform.]

Mayukh Banik

Numerade Educator

Problem 84

You are standing $1.2 \mathrm{m}$ from a heat lamp that draws an rms current of $12.5 \mathrm{A}$ when connected to $120 \mathrm{V}$ rms.
(a) Assuming that the energy of the heat lamp is radiated uniformly in a hemispherical pattern, what is the intensity of the light on your face? (b) If you stand in front of the heat lamp for 2.0 min, how much energy is incident on your face? Assume your face has a total area of $2.8 \times 10^{-2} \mathrm{m}^{2}$.
(c) What are the rms electric and magnetic fields?

Narayan Hari

Numerade Educator

Problem 85

An EM wave is generated by a magnetic dipole antenna as shown in the figure. The current in the antenna is produced by an $L C$ resonant circuit. The wave is detected at a distant point $P .$ Using the coordinate system in the figure, write equations for the $x$ -, $y$ -, and $z$ -components of the EM fields at a distant point $P$. (If there is more than one possibility, just give one consistent set of answers.) Define all quantities in your equations in terms of $L, C, E_{\mathrm{m}}$ (the electric field amplitude at point $P$ ), and universal constants.

Manish Jain

Numerade Educator

Problem 86

A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius $5.0 \mathrm{cm} .$ The EM wave has frequency $870 \mathrm{kHz}$, electric field amplitude $0.50 \mathrm{V} / \mathrm{m},$ and magnetic field amplitude $1.7 \times 10^{-9} \mathrm{T}$
(a) For best results, should the axis of the coil be aligned with the electric field of the wave, or with the magnetic field, or with the direction of propagation of the wave? (b) Assuming it is aligned correctly, what is the amplitude of the induced emf in the coil? (Since the wavelength of this wave is much larger than $5.0 \mathrm{cm},$ it can be assumed that at any instant the fields are uniform within the coil.) (c) What is the amplitude of the emf induced in an electric dipole antenna of length $5.0 \mathrm{cm}$ aligned with the electric field of the wave?

Mayukh Banik

Numerade Educator