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Physics

James S. Walker

Chapter 25

Electromagnetic Waves - all with Video Answers

Educators


Chapter Questions

04:26

Problem 1

$\cdot$ CE If the electric field in an electromagnetic wave is increasing in
magnitude at a particular time, is the magnitude of the magnetic
field at the same time increasing or decreasing? Explain.

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06:10

Problem 2

$\cdot$ The electric field of an electromagnetic wave points in the positive $y$ direction. At the same time, the magnetic field of this wave
points in the positive $z$ direction. In what direction is the wave
traveling?

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06:31

Problem 3

$\cdot$ An electric charge on the $x$ axis oscillates sinusoidally about the
origin. A distant observer is located at a point on the $+z$ axis. (a) In
what direction will the electric field oscillate at the observer's location? (b) In what direction will the magnetic field oscillate at the
observer's location? (c) In what direction will the electromagnetic
wave propagate at the observer's location?

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05:46

Problem 4

$\cdot$ An electric charge on the $y$ axis oscillates sinusoidally about the
origin. A distant observer is located at a point on the $+x$ axis. (a) In
what direction will the electric field oscillate at the observer's location? (b) In what direction will the magnetic field oscillate at the
observer's location? (c) In what direction will the electromagnetic
wave propagate at the observer's location?

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04:29

Problem 5

$\because$ Give the direction $(\mathrm{N}, \mathrm{S}, \mathrm{E}, \mathrm{W},$ up, or down $)$ of the missing quantity for each of the four electromagnetic waves listed in Table $25-1 .$

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06:33

Problem 6

$\because$ Give the direction $( \pm x, \pm y, \pm z)$ of the missing quantity for
each of the four electromagnetic waves listed in Table $25-2 .$

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04:08

Problem 7

$\cdot$ CE Three electromagnetic waves have electric and magnetic
fields pointing in the directions shown in FIGURE $25-37 .$ For each
of the three cases, state whether the wave propagates in the
$+x,-x,+y,-y,+z,$ or $-z$ direction.

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08:27

Problem 8

$\cdot$ The light-year (ly) is a unit of distance commonly used in astronomy. It is defined as the distance traveled by light in a vacuum in
one year. (a) Express 1 ly in km. (b) Express the speed of light, $c$ , in
units of ly per year. (c) Express the speed of light in feet per nanosecond.

Alex Moore
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03:53

Problem 9

$\cdot$ Alpha Centauri, the closest star to the Sun, is 4.3 ly away. How
far is this in meters?

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02:32

Problem 10

$\cdot$ Mars Rover When the Mars rover Sojourner was deployed on the
surface of Mars in July 1997 , radio signals took about 12 min to
travel from Earth to the rover. How far was Mars from Earth at that
time?

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04:57

Problem 11

A fighter jet is traveling at 515 $\mathrm{m} / \mathrm{s}$ directly away from a communication antenna that broadcasts at 406 $\mathrm{MHz} .$ What change in
frequency does the fighter jet observe?

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04:28

Problem 12

$\because$ A distant star is traveling directly away from Earth with a speed
of $49,500 \mathrm{km} / \mathrm{s} .$ By what factor are the wavelengths in this star's
spectrum changed?

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02:20

Problem 13

$\bullet$ Predict/Calculate The frequency of light reaching Earth from
a particular galaxy is 15$\%$ lower than the frequency the light had
when it was emitted. (a) Is this galaxy moving toward or away
from Earth? Explain. (b) What is the speed of this galaxy relative
to the Earth? Give your answer as a fraction of the speed of light.

Alex Moore
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04:45

Problem 14

$\because$ Predict/Calculate When an airplane communicates with a satellite using a frequency of $1.535 \times 10^{9} \mathrm{Hz}$ , the signal received by
the satellite is shifted higher by 207 $\mathrm{Hz}$ (a) Is the airplane moving
toward or away from the satellite? Explain. (b) What is the component of the airplane's velocity toward or away from the satellite?

Alex Moore
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02:53

Problem 15

$\because$ Measuring the Speed of Light Galileo attempted to measure the
speed of light by measuring the time elapsed between his opening
a lantern and his seeing the light return from his assistant's lantern. The experiment is illustrated in FIGURE $25-38 .$ What distance,
$d,$ must separate Galileo and his assistant in order for the human
reaction time, $\Delta t=0.2 \mathrm{s},$ to introduce no more than a 15$\%$ error
in the speed of light?

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03:17

Problem 16

$\cdot$ Measuring the Speed of Light: Michelson In $1926,$ Albert Michelson
measured the speed of light with a technique similar to that used
by Fizeau. Michelson used an eight-sided mirror rotating at 528
rev/s in place of the toothed wheel, as illustrated in FIGURE $25-39$ .
The distance from the rotating mirror to a distant reflector was
35.5 $\mathrm{km} .$ If the light completed the 71.0 -km round trip in the time
it took the mirror to complete one-eighth of a revolution, what is
the speed of light?

Alex Moore
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02:39

Problem 17

$\bullet$ Communicating with the Voyager Spacecraft The Voyager 1 spacecraft has traveled farther than any other man-made object, and in
August 2012 it entered into interstellar space when it was a distance
of $1.8 \times 10^{13} \mathrm{m}$ from Earth. How many hours elapsed between the
time a command was sent from Earth and the time the command
was received by Voyager when it entered interstellar space?

Alex Moore
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03:11

Problem 18

$\bullet$ A father and his daughter are interested in the same baseball
game. The father sits next to his radio at home and listens to
the game; his daughter attends the game and sits in the outfield
bleachers. In the bottom of the ninth inning a home run is hit.
If the father's radio is 132 $\mathrm{km}$ from the radio station, and the
daughter is 115 $\mathrm{m}$ from home plate, who hears the home run first?
(Assume that there is no time delay between the baseball being hit
and its sound being broadcast by the radio station. In addition, let
the speed of sound in the stadium be 343 $\mathrm{m} / \mathrm{s.}$ .

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05:27

Problem 19

$\because$ Predict/Calculate (a) How fast would a motorist have to be
traveling for a yellow $(\lambda=590 \mathrm{nm})$ traffic light to appear green
$(\lambda=550 \mathrm{nm})$ because of the Doppler shift? (b) Should the motorist be traveling toward or away from the traffic light to see this
effect? Explain.

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02:56

Problem 20

$\bullet$ Most of the galaxies in the universe are observed to be moving
away from Earth. Suppose a particular galaxy emits orange light
with a frequency of $5.000 \times 10^{14}$ Hz. If the galaxy is receding from
Earth with a speed of 4375 $\mathrm{km} / \mathrm{s}$ , what is the frequency of the light
when it reaches Earth?

Alex Moore
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03:49

Problem 21

$\bullet$ Two starships, the Enterprise and the Constitution, are approaching each other head-on from a great distance. The separation
between them is decreasing at a rate of 782.5 $\mathrm{km} / \mathrm{s}$ . The Enterprise
sends a laser signal toward the Constitution. If the Constitution
observes a wavelength $\lambda=670.3 \mathrm{nm},$ what wavelength was emitted by the Enterprise?

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05:36

Problem 22

$\because$ Baseball scouts often use a radar gun to measure the speed of
a pitch. One particular model of radar gun emits a microwave
signal at a frequency of 10.525 GHz. What will be the increase in
frequency if these waves are reflected from a $95.0-$ mi/h fastball
headed straight toward the gun? (Note: $1 \mathrm{mi} / \mathrm{h}=0.447 \mathrm{m} / \mathrm{s}$ )

Alex Moore
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05:02

Problem 23

$\bullet$ A state highway patrol car radar unit uses a frequency of
$8.00 \times 10^{9}$ Hz. What frequency difference will the unit detect from
a car receding at a speed of 64.5 $\mathrm{m} / \mathrm{s}$ from a stationary patrol car?

Alex Moore
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05:55

Problem 24

$\bullet$ Consider a spiral galaxy that is moving directly away from Earth
with a speed $V=3.240 \times 10^{5} \mathrm{m} / \mathrm{s}$ at its center, as shown in FIGURE
$25-40 .$ The galaxy is also rotating about its center, such that points
in its spiral arms are moving with a speed $v=5.750 \times 10^{5} \mathrm{m} / \mathrm{s}$ relative to the center. If light with a frequency of $7.308 \times 10^{14} \mathrm{Hz}$ is
emitted in both arms of the galaxy, what frequency is detected by
astronomers observing the arm that is moving (a) toward and
(b) away from Earth? (Measurements of this type are used to map
out the speed of various regions in distant, rotating galaxies.)

Alex Moore
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05:14

Problem 25

$\cdots \bullet$ Predict/Calculate A highway patrolman sends a $28.250-$ GHz
radar beam toward a speeding car. The reflected wave is lower in
frequency by 2.97 $\mathrm{kHz}$ . (a) Is the car moving toward or away from
the radar gun? Explain. (b) What is the speed of the car? [Hint:
For small values of $x,$ the following approximation may be used:
$(1+x)^{2} \approx 1+2 x . ]$

Alex Moore
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01:44

Problem 26

$\cdot$ BIO Dental $\mathrm{X}$ -rays The X-rays produced in the dentist's office typically have a wavelength of 0.30 nm. What is the frequency of these
rays?

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02:05

Problem 27

Find the frequency of green light with a wavelength of 555 $\mathrm{nm} .$

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01:47

Problem 28

$\cdot$ Yellow light has a wavelength $\lambda=590 \mathrm{nm} .$ How many of these
waves would span the 1.35 -mm thickness of a dime?

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02:02

Problem 29

$\cdot$ How many red wavelengths $(\lambda=705 \mathrm{nm})$ tall are you?

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01:54

Problem 30

$\cdot$ A cell phone transmits at a frequency of $1.94 \times 10^{9} \mathrm{Hz} .$ What is
the wavelength of the electromagnetic wave used by this phone?

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01:32

Problem 31

$\cdot$ Microwave Oven If a microwave oven produces electromagnetic
waves with a frequency of 2.45 $\mathrm{GHz}$ , what is their wavelength?

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02:35

Problem 32

$\cdot$ BIO Human Radiation Under normal conditions, humans radiate
electromagnetic waves with a wavelength of about 9.0 microns.
(a) What is the frequency of these waves? (b) To what portion of
the electromagnetic spectrum do these waves belong?

Alex Moore
Alex Moore
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03:32

Problem 33

$\cdot$ BIO UV Radiation Ultraviolet light is typically divided into three
categories. UV-A, with wavelengths between 400 $\mathrm{nm}$ and 320 $\mathrm{nm}$ ,
has been linked with malignant melanomas. UV-B radiation,
which is the primary cause of sunburn and other skin cancers,
has wavelengths between 320 $\mathrm{nm}$ and 280 $\mathrm{nm}$ . Finally, the region
known as UV-C extends to wavelengths of 100 $\mathrm{nm}$ . (a) Find the
range of frequencies for UV-B radiation. (b) In which of these
three categories does radiation with a frequency of $7.9 \times 10^{14} \mathrm{Hz}$
belong?

Alex Moore
Alex Moore
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02:07

Problem 34

$\cdot$ Communicating with a Submarine Normal radiofrequency waves
cannot penetrate more than a few meters below the surface of the
ocean. One method of communicating with submerged submarines uses very low frequency (VLF) radio waves. What is the wave-length (in air) of a 10.0 -kHz VLF radio wave?

Alex Moore
Alex Moore
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02:07

Problem 35

$\bullet$ Predict/Calculate When an electromagnetic wave travels from
one medium to another with a different speed of propagation, the
frequency of the wave remains the same. Its wavelength, however,
changes. (a) If the wave speed decreases, does the wavelength increase
or decrease? Explain. (b) Consider a case where the wave speed
decreases from $c$ to $\frac{3}{4} c .$ By what factor does the wavelength change?

Alex Moore
Alex Moore
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04:08

Problem 36

$\bullet$ Predict/Calculate (a) Which color of light has the higher frequency, red or violet? (b) Calculate the frequency of blue light with
a wavelength of 470 $\mathrm{nm}$ , and red light with a wavelength of 680 $\mathrm{nm}$ .

Alex Moore
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02:25

Problem 37

$\bullet$ ULF (ultra low frequency) electromagnetic waves, produced in
the depths of outer space, have been observed with wavelengths in
excess of 29 million kilometers. What is the period of such a wave?

Alex Moore
Alex Moore
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01:52

Problem 38

$\cdots$ A television is tuned to a station broadcasting at a frequency of
$2.04 \times 10^{8}$ Hz. For best reception, the rabbit-ear antenna used by
the TV should be adjusted to have a tip-to-tip length equal to half
a wavelength of the broadcast signal. Find the optimum length of
the antenna.

Alex Moore
Alex Moore
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02:03

Problem 39

$\because$ An AM radio station's antenna is constructed to be $\lambda / 4$ tall,
where $\lambda$ is the wavelength of the radio waves. How tall should the
antenna be for a station broadcasting at a frequency of 810 $\mathrm{kHz}$ ?

Alex Moore
Alex Moore
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02:39

Problem 40

$\because$ As you drive by an AM radio station, you notice a sign saying
that its antenna is 112 $\mathrm{m}$ high. If this height represents one quarter-wavelength of its signal, what is the frequency of the station?

Alex Moore
Alex Moore
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04:54

Problem 41

$\bullet$ Find the difference in wavelength $\left(\lambda_{1}-\lambda_{2}\right)$ for each of the following pairs of radio waves: (a) $f_{1}=50 \mathrm{kHz}$ and $f_{2}=52 \mathrm{kHz}$
(b) $f_{1}=500 \mathrm{kHz}$ and $f_{2}=502 \mathrm{kHz}$

Alex Moore
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08:10

Problem 42

$\cdots$ Synchrotron Frequency In one portion of a synchrotron, electrons
traveling at $2.99 \times 10^{8} \mathrm{m} / \mathrm{s}$ entera region of uniform magnetic field
with a strength of 0.599 $\mathrm{T}$ . (a) What is the acceleration of an electron in this region? (Ignore the effects of relativity.) (b) The largest
amount of light is emitted by the synchrotron at a frequency given
by $f=(0.0433) a \mathrm{Hz},$ where $a$ is the acceleration in $\mathrm{m} / \mathrm{s}^{2} .$ What are this frequency and its corresponding wavelength? In what portion
of the electromagnetic spectrum do these waves belong?

Alex Moore
Alex Moore
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04:14

Problem 43

$\cdot$ CE If the rms value of the electric field in an electromagnetic
wave is doubled, (a) by what factor does the rms value of the magnetic field change? (b) By what factor does the average intensity of
the wave change?

Alex Moore
Alex Moore
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03:36

Problem 44

$\cdot$ CE The radiation pressure exerted by beam of light 1 is half the
radiation pressure of beam of light 2. If the rms electric field of
beam 1 has the value $E_{0},$ what is the rms electric field in beam 2 ?

Alex Moore
Alex Moore
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02:34

Problem 45

$\cdot$ The maximum magnitude of the electric field in an electromagnetic wave is 0.0675 $\mathrm{V} / \mathrm{m} .$ What is the maximum magnitude of
the magnetic field in this wave?

Alex Moore
Alex Moore
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01:03

Problem 46

$\cdot$ What is the rms value of the electric field in a sinusoidal electromagnetic wave that has a maximum electric field of 99 $\mathrm{V} / \mathrm{m}$ ?

Alex Moore
Alex Moore
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06:54

Problem 47

$. .$ The magnetic field in an electromagnetic wave has a peak value
given by $B=2.9 \mu \mathrm{T} .$ For this wave, find (a) the peak electric field
strength, (b) the peak intensity, and (c) the average intensity.

Alex Moore
Alex Moore
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01:18

Problem 48

$\bullet$ What is the maximum value of the electric field in an electromagnetic wave whose maximum intensity is 7.55 $\mathrm{W} / \mathrm{m}^{2} ?$

Nishant Kumar
Nishant Kumar
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03:36

Problem 49

$\bullet$ What is the maximum value of the electric field in an electromagnetic wave whose average intensity is 7.55 $\mathrm{W} / \mathrm{m}^{2} ?$

Alex Moore
Alex Moore
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04:57

Problem 50

$\bullet$ Predict/Calculate Electromagnetic wave 1 has a maximum
electric field of $E_{0}=52 \mathrm{V} / \mathrm{m},$ and electromagnetic wave 2 has a
maximum magnetic field of $B_{0}=1.5 \mu \mathrm{T}$ (a) Which wave has the
greater intensity? (b) Calculate the intensity of each wave.

Alex Moore
Alex Moore
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03:44

Problem 51

$\because \mathrm{A} 75$ -kW radio station broadcasts its signal uniformly in all directions. (a) What is the average intensity of its signal at a distance of
250 $\mathrm{m}$ from the antenna? (b) What is the average intensity of its
signal at a distance of 2500 $\mathrm{m}$ from the antenna?

Alex Moore
Alex Moore
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03:18

Problem 52

$\bullet$ At what distance will a $45-W$ lightbulb have the same apparent brightness as a $120-\mathrm{W}$ bulb viewed from a distance of 25 $\mathrm{m}$ ?
(Assume that both bulbs convert electrical power to light with the
same efficiency, and radiate light uniformly in all directions.)

Alex Moore
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02:58

Problem 53

$\bullet$ What is the ratio of the sunlight intensity reaching Pluto compared with the sunlight intensity reaching Earth? (On average,
Pluto is 39 times as far from the Sun as is Earth.)

Alex Moore
Alex Moore
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02:53

Problem 54

$\bullet$ Predict/Calculate In the following, assume that lightbulbs
radiate uniformly in all directions and that 5.0$\%$ of their power is
converted to light.(a) Find the average intensity of light at a point
2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ red lightbulb $(\lambda=710 \mathrm{nm}) .$ (b) Is the average intensity 2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ blue lightbulb $(\lambda=480 \mathrm{nm})$
greater than, less than, or the same as the intensity found in part
(a)? Explain. (c) Calculate the average intensity for part (b).

Alex Moore
Alex Moore
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02:29

Problem 55

$\because \mathrm{A} 7.7-\mathrm{mW}$ laser produces a narrow beam of light. How much
energy is contained in a $1.0-\mathrm{m}$ length of its beam?

Alex Moore
Alex Moore
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03:06

Problem 56

$\bullet$ What length of a 7.7 -mW laser's beam will contain 9.5 $\mathrm{mJ}$ of
energy?

Alex Moore
Alex Moore
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02:31

Problem 57

Sunlight Intensity After filtering through the atmosphere,
the Sun's radiation illuminates Earth's surface with an average intensity of 1.0 $\mathrm{kW} / \mathrm{m}^{2}$ . Assuming this radiation strikes the
$15-\mathrm{m} \times 45-\mathrm{m}$ black, flat roof a building at normal incidence,
calculate the average force the radiation exerts on the roof.

Alex Moore
Alex Moore
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05:04

Problem 58

$\bullet$ Predict/Calculate (a) Find the electric and magnetic field
amplitudes in an electromagnetic wave that has an average energy
density of 1.0 $\mathrm{J} / \mathrm{m}^{3} .$ (b) By what factor must the field amplitudes be
increased if the average energy density is to be doubled to 2.0 $\mathrm{J} / \mathrm{m}^{3} ?$

Alex Moore
Alex Moore
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04:41

Problem 59

$\cdots$ Lasers for Fusion Some of the most powerful lasers in the world
are used in nuclear fusion experiments. The NOVA laser produced
40.0 $\mathrm{kJ}$ of energy in a pulse that lasted 2.50 $\mathrm{ns}$ , and the NIF laser
produces a 20.0 -ns pulse with 4.20 $\mathrm{MJ}$ of energy. (a) Which laser
produces more energy in each pulse? (b) Which laser produces the
greater average power during each pulse? (c) If the beam diameters
are the same, which laser produces the greater average intensity?

Alex Moore
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05:15

Problem 60

$\because$ B1o You are standing 2.5 $\mathrm{m}$ from a $150-\mathrm{W}$ lightbulb. (a) If the
pupil of your eye is a circle 5.0 $\mathrm{mm}$ in diameter, how much energy
enters your eye per second? (Assume that 5.0$\%$ of the lightbulb's
power is converted to light.) (b) Repeat part (a) for the case of a
1.0 -mm-diameter laser beam with a power of 0.50 $\mathrm{mW}$ .

Nathan Silvano
Nathan Silvano
Numerade Educator
06:11

Problem 61

$\bullet$ BIO Laser Safety A 0.75 -mW laser
emits a narrow beam of light that
enters the eye, as shown in FlGURE 25 -41. (a) How much
energy is absorbed
by the eye in 0.2 s? (b) The eye focuses this beam to a tiny spot on
the retina, perhaps 5.0$\mu \mathrm{m}$ in diameter. What is the average intensity of light $\left($ in $\mathrm{W} / \mathrm{cm}^{2}\right)$ at this spot? (c) Damage to the retina can
occur if the average intensity of light exceeds $1.0 \times 10^{-2} \mathrm{W} / \mathrm{cm}^{2} .$
By what factor has the intensity of this laser beam exceeded the
safe value?

Nathan Silvano
Nathan Silvano
Numerade Educator
05:16

Problem 62

$\bullet$ Find the rms electric and magnetic fields at a point 2.50 $\mathrm{m}$ from
a lightbulb that radiates 115 $\mathrm{W}$ of light uniformly in all directions.

Nathan Silvano
Nathan Silvano
Numerade Educator
06:00

Problem 63

$\bullet \mathrm{A} 0.50$ -mw laser produces a beam of light with a diameter of
1.5 mm.(a) What is the average intensity of this beam? (b) At what
distance does a $150-$ W lightbulb have the same average intensity as
that found for the laser beam in part (a)? (Assume that 5.0$\%$ of the
bulb's power is converted to light.)

Nathan Silvano
Nathan Silvano
Numerade Educator
04:26

Problem 64

$\cdots$ A laser emits a cylindrical beam of light 3.4 $\mathrm{mm}$ in diameter. If
the average power of the laser is $2.5 \mathrm{mW},$ what is the rms value of
the electric field in the laser beam?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:31

Problem 65

$\because$ (a) If the laser in Problem 64 shines its light on a perfectly
absorbing surface, how much energy does the surface receive in
12 s? (b) What is the radiation pressure exerted by the beam?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:39

Problem 66

$\cdots \cdot$ BIO Laser Surgery Each pulse produced by an argon-fluoride
excimer laser used in PRK and LASIK ophthalmic surgery lasts only
10.0 ns but delivers an energy of 2.50 $\mathrm{mJ}$ . (a) What is the power
produced during each pulse? (b) If the beam has a diameter of
$0.850 \mathrm{mm},$ what is the average intensity of the beam during each
pulse? (c) If the laser emits 55 pulses per second, what is the average power it generates?

Nathan Silvano
Nathan Silvano
Numerade Educator
04:10

Problem 67

$\cdots$ A pulsed laser produces brief bursts of light. One such laser
emits pulses that carry 0.350 J of energy but last only 225 fs. (a) What
is the average power during one of these pulses? (b) Assuming the
energy is emitted in a cylindrical beam of light 2.00 $\mathrm{mm}$ in diameter, calculate the average intensity of this laser beam. (c) What is
the rms electric field in this wave?

Nishant Kumar
Nishant Kumar
Numerade Educator
02:30

Problem 68

$\cdot$ CE Predict/Explain Consider the two polarization experiments
shown in FIGURE $25-42 .$ (a) If the incident light is unpolarized, is the
transmitted intensity in case A greater than, less than, or the same
as the transmitted intensity in case $B ?$ (b) Choose the best explanation from among the following:
I. The transmitted intensity is the same in either case; the first
polarizer lets through one-half the incident intensity, and the
second polarizer is at an angle $\theta$ relative to the first.
II. Case A has a smaller transmitted intensity than case B because
the first polarizer is at an angle $\theta$ relative to the incident beam.
III. Case $B$ has a smaller transmitted intensity than case A because
the direction of polarization is rotated by an angle $\theta$ in the
clockwise direction in case B.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:52

Problem 69

$\cdot$ CE Predict/Explain Consider the two polarization experiments
shown in Figure $25-42 .$ (a) If the incident light is polarized in the
horizontal direction, is the transmitted intensity in case A greater
than, less than, or the same as the transmitted intensity in case B?
(b) Choose the best explanation from among the following:
I. The two cases have the same transmitted intensity because
the angle between the polarizers is $\theta$ in each case.
II. The transmitted intensity is greater in case B because all of the
initial beam gets through the first polarizer.
III. The transmitted intensity in case $B$ is smaller than in case $A ;$ in
fact, the transmitted intensity in case $B$ is zero because the
first polarizer is oriented vertically.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:11

Problem 70

$\cdot \mathrm{CE}$ An incident beam of
light with an intensity $I_{0}$
passes through a polarizing filter whose transmission axis is at an angle $\theta$ to
the vertical. As the angle
is changed from $\theta=0$ to
$\theta=90^{\circ},$ the intensity as a
function of angle is given
by one of the curves in FIGURE $25-43 .$ Give the color of
the curve corresponding to an incident beam that is (a) unpolarized, (b) vertically polarized, and (c) horizontally polarized.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:14

Problem 71

$\cdot$ Vertically polarized light with an intensity of 0.55 $\mathrm{W} / \mathrm{m}^{2}$ passes
through a polarizer whose transmission axis is at an angle of
$85.0^{\circ}$ with the vertical. What is the intensity of the transmitted
light?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:03

Problem 72

$\cdot$ A person riding in a boat observes that the sunlight reflected
by the water is polarized parallel to the surface of the water. The
person is wearing polarized sunglasses with the polarization axis
vertical. If the wearer leans at an angle of $21.5^{\circ}$ to the vertical,
what fraction of the reflected light intensity will pass through
the sunglasses?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:45

Problem 73

$\bullet$ Unpolarized light passes through two polarizers whose transmission axes are at an angle of $30.0^{\circ}$ with respect to each other. What fraction of the incident intensity is transmitted through the polarizers?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:11

Problem 74

$\because$ In Problem $73,$ what should be the angle between the transmission axes of the polarizers if it is desired that one-tenth of the incident intensity be transmitted?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:58

Problem 75

$\cdots$ EE Unpolarized light is incident with intensity $I_{0}$ on a polarizer
whose transmission axis is vertical, as in Figure $25-26 .$ It then falls
on an analyzer whose transmission axis is at an angle $\theta$ to the vertical. Which of the graphs in FIGURE $25-44$ depicts the transmitted
intensity as $\theta$ is changed from $0^{\circ}$ to $360^{\circ} ?$

Nathan Silvano
Nathan Silvano
Numerade Educator
06:33

Problem 76

$\because$ Predict/Calculate A beam of vertically polarized light encounters two polarizing filters, as shown in FIGURE $25-45$ . (a) Rank the three cases, $\mathrm{A}, \mathrm{B},$ and $\mathrm{C},$ in order of increasing transmitted intensity. Indicate ties where appropriate. (b) Calculate the transmitted
intensity for each of the cases in Figure $25-45,$ assuming that the incident intensity is 55.5 $\mathrm{W} / \mathrm{m}^{2} .$ Verify that your numerical results
agree with the rankings in part (a).

Nathan Silvano
Nathan Silvano
Numerade Educator
05:28

Problem 77

$\because$ Predict/Calculate Repeat Problem $76,$ this time assuming that
the polarizers to the left in Figure $25-45$ are at an angle of $22.5^{\circ}$ to the
vertical rather than $45^{\circ} .$ The incident intensity is again 55.5 $\mathrm{W} / \mathrm{m}^{2}$ .

Nathan Silvano
Nathan Silvano
Numerade Educator
03:40

Problem 78

$\because$ BIO Predict/Calculate Optical Activity Optically active molecules
have the property of rotating the direction of polarization of linearly
polarized light. Many biologically important molecules have this
property, some causing a counterclockwise rotation (negative rotation angle), others causing a clockwise rotation (positive rotation
angle). For example, a 5.00 gram per 100 mL solution of l-leucine
causes a rotation of $-0.550^{\circ}$ ; the same concentration of $d$ -glutamic
acid causes a rotation of $0.620^{\circ} .$ (a) If placed between crossed polarizers, which of these solutions transmits the greater intensity?
Explain. (b) Find the transmitted intensity for each of these solutions when placed between crossed polarizers. The incident beam is
unpolarized and has an intensity of 12.5 $\mathrm{W} / \mathrm{m}^{2}$ .

Nathan Silvano
Nathan Silvano
Numerade Educator
04:59

Problem 79

$\bullet$ A helium-neon laser emits a beam of unpolarized light that
passes through three Polaroid filters, as shown in FIGURE $25-46$ . The
intensity of the laser beam is $I_{0}$ . (a) What is the intensity of the
beam at point $\mathrm{A} ?$ (b) What is the intensity of the beam at point
B? (c) What is the intensity of the beam at point $C ?$ (d) If filter 2 is
removed, what is the intensity of the beam at point C?

Nathan Silvano
Nathan Silvano
Numerade Educator
09:10

Problem 80

$\cdots \cdot$ Referring to Figure $25-46,$ suppose that filter 3 is at a general
angle $\theta$ with the vertical, rather than the angle $90^{\circ} .$ (a) Find an
expression for the transmitted intensity as a function of $\theta$ . (b) Plot
your result from part (a), and determine the maximum transmitted
intensity. (c) At what angle $\theta$ does maximum transmission occur?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:58

Problem 81

$\cdot$ CE Suppose the magnitude of the electric field in an electromagnetic wave is doubled. (a) By what factor does the magnitude of
the magnetic field change? (b) By what factor does the maximum
intensity of the wave change?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:37

Problem 82

$\cdot$ CE If "sailors" of the future use radiation pressure to propel their
ships, should the surfaces of their sails be absorbing or reflecting?
Explain.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:22

Problem 83

$\cdot$ BIO A typical medical X-ray has a frequency of $1.50 \times 10^{19} \mathrm{Hz}$
What is the wavelength of such an X-ray?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:23

Problem 84

$\cdot$ BIO Radiofrequency Ablation In radiofrequency (RF) ablation, a
small needle is inserted into a cancerous tumor. When radiofrequency oscillating currents are sent into the needle, ions in the
neighboring tissue respond by vibrating rapidly, causing local
heating to temperatures as high as $100^{\circ} \mathrm{C}$ . This kills the cancerous cells and, because of the small size of the needle, relatively few
of the surrounding healthy cells. A typical RF ablation treatment
uses a frequency of 750 kHz. What is the wavelength that such
radio waves would have in a vacuum?

Nathan Silvano
Nathan Silvano
Numerade Educator
07:14

Problem 85

$\bullet$ Predict/Calculate At a particular instant of time, a light beam
traveling in the positive $z$ direction has an electric field given by
$\overrightarrow{\mathbf{E}}=(6.22 \mathrm{N} / \mathrm{C}) \hat{\mathbf{x}}+(2.87 \mathrm{N} / \mathrm{C})$ . The magnetic field in the beam
has a magnitude of $2.28 \times 10^{-8} \mathrm{T}$ at the same time. (a) Does the
magnetic field at this time have a z component that is positive,
negative, or zero? Explain. (b) Write $\overrightarrow{\mathbf{B}}$ in terms of unit vectors.

Nathan Silvano
Nathan Silvano
Numerade Educator
05:56

Problem 86

$\bullet$ Predict/Calculate $A$ light beam traveling in the negative $z$ direction has a magnetic field $\overline{\mathbf{B}}=\left(3.02 \times 10^{-9} \mathrm{T}\right) \hat{\mathbf{x}}+$
$\left(-5.28 \times 10^{-9} \mathrm{T}\right) \hat{\mathbf{y}}$ at a given instant of time. The electric field in the beam has a magnitude of 1.82 $\mathrm{N} / \mathrm{C}$ at the same time. (a) Does
the electric field at this time have a $z$ component that is positive,
negative, or zero? Explain. (b) Write $\overline{\mathbf{E}}$ in terms of unit vectors.

Nathan Silvano
Nathan Silvano
Numerade Educator
03:34

Problem 87

$\bullet$ CE FIGURE $25-47$ shows four polarization experiments in which
unpolarized incident light passes through two polarizing filters
with different orientations. Rank the four cases in order of increasing amount of transmitted light. Indicate ties where appropriate.

Nathan Silvano
Nathan Silvano
Numerade Educator
03:00

Problem 88

$\bullet$ Lightning and Thunder During a thunderstorm a bolt of lightning strikes 2.41 $\mathrm{km}$ away from you. (a) How much time elapses
between when the lightning strikes and when the light reaches
your eyes? (b) If the speed of sound is $343 \mathrm{m} / \mathrm{s},$ how much time
elapses before the sound of thunder reaches your ears?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:19

Problem 89

$\bullet$ The Apollo 11 Reflector One of the experiments placed on the
Moon's surface by Apollo 11 astronauts was a reflector that is
used to measure the Earth-Moon distance with high accuracy. A
laser beam on Earth is bounced off the reflector, and its round-trip travel time is recorded. If the travel time can be measured to
within an accuracy of 0.030 $\mathrm{ns}$ , what is the uncertainty in the
Earth-Moon distance?

Nathan Silvano
Nathan Silvano
Numerade Educator
08:13

Problem 90

$\bullet$ International Space Station The International Space Station (ISS)
orbits Earth at an altitude of 422 $\mathrm{km}$ . (a) What is its orbital speed?
(b) What is the speed of a receiving antenna on Earth's equator?
(c) Suppose the ISS is moving directly toward the antenna, and the
antenna is moving directly away from the ISS. If the ISS transmits
a radio signal at 145.8000 $\mathrm{MHz}$ , what frequency is received by the
antenna?

Nathan Silvano
Nathan Silvano
Numerade Educator
05:27

Problem 91

$\because$ Predict/Calculate Suppose the distance to the fixed mirror in
Figure $25-39$ is decreased to 20.5 $\mathrm{km} .$ (a) Should the angular speed
of the rotating mirror be increased or decreased to ensure that the
experiment works as described in Problem 16$?($ b) Find the required
angular speed, assuming the speed of light is $3.00 \times 10^{8} \mathrm{m} / \mathrm{s}$ .

Nathan Silvano
Nathan Silvano
Numerade Educator
05:36

Problem 92

$\because$ BIO Predict/Calculate Consider the physical situation illustrated in Figure $25-41 .\left($ a) Is $E_{\mathrm{rms}}$ in the incident laser beam greater \right.
than, less than, or the same as $E_{\mathrm{rms}}$ where the beam hits the retina?
Explain. (b) If the intensity of the beam at the retina is equal to
the damage threshold, $1.0 \times 10^{-2} \mathrm{W} / \mathrm{cm}^{2},$ what is the value of
$E_{\mathrm{ms}}$ at that location? (c) If the diameter of the spot on the retina is
reduced by a factor of $2,$ by what factor does the intensity increase?
By what factor does $E_{\mathrm{rms}}$ increase?

Nathan Silvano
Nathan Silvano
Numerade Educator
03:10

Problem 93

$\because$ Blo Polaroid Vision in a Spider Experiments show that the ground
spider Drassodes cupreus uses one of its several pairs of eyes as a
polarization detector. In fact, the two eyes in this pair have polarization directions that are at right angles to one another. Suppose linearly polarized light with an intensity of 775 $\mathrm{W} / \mathrm{m}^{2}$ shines from
the sky onto the spider, and that the intensity transmitted by one
of the polarizing eyes is 274 $\mathrm{W} / \mathrm{m}^{2} .$ (a) For this eye, what is the
angle between the polarization direction of the eye and the polarization direction of the incident light? (b) What is the intensity
transmitted by the other polarizing eye?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:50

Problem 94

$\bullet$ A state highway patrol car radar unit uses a frequency of
$9.00 \times 10^{9} \mathrm{Hz}$ . What frequency difference will the unit detect
from a car approaching a parked patrol car with a speed of
28.6 $\mathrm{m} / \mathrm{s}$ ?

Nathan Silvano
Nathan Silvano
Numerade Educator
01:48

Problem 95

$\bullet$ What is the ratio of the sunlight intensity reaching Mercury
compared with the sunlight intensity reaching Earth? (On average, Mercury's distance from the Sun is 0.39 that of Earth's.)

Nathan Silvano
Nathan Silvano
Numerade Educator
01:16

Problem 96

$\because$ What area is needed for a solar collector to absorb 45.0 $\mathrm{kW}$ of
power from the Sun's radiation if the collector is 75.0$\%$ efficient?
(At the surface of Earth, sunlight has an average intensity of
$1.00 \times 10^{3} \mathrm{W} / \mathrm{m}^{2} . )$

Nathan Silvano
Nathan Silvano
Numerade Educator
04:27

Problem 97

$\because$ BIO Near-Infrared Brain Scans Light in the near-infrared (close to
visible red) can penetrate surprisingly far through human tissue,
a fact that is being used to "illuminate" the interior of the brain
in a noninvasive technique known as near-infrared spectroscopy
(NIRS). In this procedure, illustrated in FIGURE $25-48,$ an optical fiber
carrying a beam of infrared laser light with a power of 1.5 $\mathrm{mW}$ and
a cross-sectional diameter of 1.2 $\mathrm{mm}$ is placed against the skull.
Some of the light enters the brain, where it scatters from hemoglobin in the blood. The scattered light is picked up by a detector
and analyzed by a computer. (a) According to the Beer-Lambert
law, the intensity of light, $I$ , decreases with penetration distance,
$d,$ as $I=I_{0} e^{-\mu d}$ , where $I_{0}$ is the initial intensity of the beam and
$\mu=4.7 \mathrm{cm}^{-1}$ fora typical case. Find the intensity of the laser beam
after it penetrates through 3.0 $\mathrm{cm}$ of tissue. (b) Find the electric
field of the initial light beam.

Nathan Silvano
Nathan Silvano
Numerade Educator
05:34

Problem 98

$\because$ Three polarizers are arranged as shown in Figure $25-46 .$ If the
incident beam of light is unpolarized and has an intensity of
$1.60 \mathrm{W} / \mathrm{m}^{2},$ find the transmitted intensity (a) when $\theta_{2}=25.0^{\circ}$
and $\theta_{3}=50.0^{\circ},$ and ( b ) when $\theta_{2}=50.0^{\circ}$ and $\theta_{3}=25.0^{\circ} .$

Nathan Silvano
Nathan Silvano
Numerade Educator
02:08

Problem 99

$\because$ Glare Reduction The light that reaches a person's eyes is a combination of 625 $\mathrm{W} / \mathrm{m}^{2}$ of unpolarized light and 282 $\mathrm{W} / \mathrm{m}^{2}$ of
horizontally polarized light. The person puts on sunglasses that are ideal polarizers with a vertical transmission axis, but also
darkening lenses that absorb 33.0$\%$ of all light. What intensity is
transmitted through these sunglasses?

Nathan Silvano
Nathan Silvano
Numerade Educator
04:58

Problem 100

$\bullet$ Orbital Drift The radiation pressure exerted by the Sun on the
Earth counteracts the gravitational attraction and puts the
Earth into an orbit that is farther from the Sun than if there
were no radiation pressure. It can be shown that the distance
added to Earth's orbital radius is given by $\left(F_{\text { rad }} / F_{g}\right) r,$ where $F_{\text { rad }}$ is
the radiation force exerted on Earth by the Sun, $F_{g}$ is the gravitational force between the Earth and Sun, and $r$ is the average orbital radius. (a) If the intensity of sunlight that strikes
Earth is $1360 \mathrm{W} / \mathrm{m}^{2},$ what is $F_{\text { rad }}$ assuming the Earth is a perfect absorber? (b) Assuming $r=1.50 \times 10^{11} \mathrm{m},$ what is $F_{\mathrm{g}}$ ?
(c) What is the additional distance added to Earth's orbital radius
by the radiation pressure?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:07

Problem 101

$\bullet$ A lightbulb emits light uniformly in all directions. If the rms
electric field of this light is 16.0 $\mathrm{N} / \mathrm{C}$ at a distance of 1.35 $\mathrm{m}$ from
the bulb, what is the average total power radiated by the bulb?

Nathan Silvano
Nathan Silvano
Numerade Educator
04:13

Problem 102

$\because$ Radio Reception $A 125-\mathrm{kW}$ radio station broadcasts its signal
uniformly in all directions. (a) What is the average intensity of its
signal at a distance of 8.05 $\mathrm{km}$ from the station? (b) What is the
rms value of the electric field in this radio wave? (c) If a $1.22-\mathrm{m}$
receiving antenna is oriented parallel to the electric field of the
radio wave, what rms voltage appears between its ends?

Nathan Silvano
Nathan Silvano
Numerade Educator
06:59

Problem 103

$\cdots$ Light Rocket Stranded 12 $\mathrm{m}$ from your spacecraft, you realize
that your flashlight makes a directed beam of intensity 950 $\mathrm{W} / \mathrm{m}^{2}$
and can be used to propel you back to safety. (a) If the radius of
the beam is $3.8 \mathrm{cm},$ how much force does it exert on you? (b) If
your mass (with spacesuit and gear) is 95 $\mathrm{kg}$ , what acceleration
does the flashlight give you? (c) How much time will it take for
you to reach the spacecraft? (d) Frustrated by the slow pace, you
throw the 0.82 -kg flashlight at 22 $\mathrm{m} / \mathrm{s}$ directly away from the
spacecraft. In how much time will you reach the spacecraft after
you throw the flashlight?

Nathan Silvano
Nathan Silvano
Numerade Educator
02:14

Problem 104

\cdots. A typical home may require a total of $2.00 \times 10^{3} \mathrm{kWh}$
of energy per month. Suppose you would like to obtain this
energy from sunlight, which has an average daylight intensity of
$1.00 \times 10^{3} \mathrm{W} / \mathrm{m}^{2} .$ Assuming that sunlight is available 8.0 $\mathrm{h}$ per day, 25 d per month (accounting for cloudy days), and that you
have a way to store energy from your collector when the Sun isn't
shining, determine the smallest collector size that will provide
the needed energy, given a conversion efficiency of 25$\% .$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:51

Problem 105

$\cdots$ At the top of Earth's atmosphere, sunlight has an average
intensity of 1360 $\mathrm{W} / \mathrm{m}^{2} .$ If the average distance from Earth to the
Sun is $1.50 \times 10^{11} \mathrm{m},$ at what rate does the Sun radiate energy?

Nathan Silvano
Nathan Silvano
Numerade Educator
06:28

Problem 106

$\cdots \bullet$ Predict/Calculate A typical laser used in introductory physics laboratories produces a continuous beam of light about 1.0 $\mathrm{mm}$
in diameter. The average power of such a laser is 0.75 $\mathrm{mW} .$ What
are (a) the average intensity, (b) the peak intensity, and (c) the
average energy density of this beam? (d) If the beam is reflected
from a mirror, what is the maximum force the laser beam can
exert on it? (e) Describe the orientation of the laser beam relative
to the mirror for the case of maximum force.

Nathan Silvano
Nathan Silvano
Numerade Educator
06:06

Problem 107

$\cdots$ Four polarizers are set up so that the transmission axis of each
successive polarizer is rotated clockwise by an angle $\theta$ relative to
the previous polarizer. Find the angle $\theta$ for which unpolarized
light is transmitted through these four polarizers with its intensity reduced by a factor of $25 .$

Nathan Silvano
Nathan Silvano
Numerade Educator
04:39

Problem 108

$\cdots \bullet$ BIO Optical Activity of Sugar The sugar concentration in a solution (e.g., in a urine specimen) can be measured conveniently
by using the optical activity of sugar and other asymmetric molecules. In general, an optically active molecule, like sugar, will
rotate the plane of polarization through an angle that is proportional to the thickness of the sample and to the concentration of the molecule. To measure the concentration of a given
solution, a sample of known thickness is placed between two
polarizing filters that are at right angles to each other, as shown
in FIGURE $25-49 .$ The intensity of light transmitted through the two
filters can be compared with a calibration chart to determine
the concentration. (a) What percentage of the incident (unpolarized) light will pass through the first filter? (b) If no sample is
present, what percentage of the initial light will pass through the
second filter? (c) When a particular sample is placed between the
two filters, the intensity of light emerging from the second filter
is 40.0$\%$ of the incident intensity. Through what angle did the
sample rotate the plane of polarization? (d) A second sample has
half the sugar concentration of the first sample. Find the intensity
of light emerging from the second filter in this case.

Nathan Silvano
Nathan Silvano
Numerade Educator
01:21

Problem 109

An essential part of modern dentistry is visible-light curing (VLC),
a procedure that hardens the restorative materials used in fillings, veneers, and other applications. These "curing lights" work
by activating molecules known as photoinitiators within the restorative materials. The photoinitiators, in turn, start a process of
polymerization that causes monomers to link together to form a
tough, solid polymer network. Thus, with VLC a dentist can apply
and shape soft restorative materials as desired, shine a bright light
on the result as shown in FIGURE $25-50(a),$ and in 20 seconds have a
completely hardened - or cured- final product.
The most common photoinitiator is camphoroquinone (CPQ).
To cure CPQ in the least time, one should illuminate it with light
having a wavelength that matches the wavelength at which CPQ
absorbs the most light. A rough plot of the relative absorption of
CPQ for light of different wavelengths is shown in FIGURE $25-50$ (b).
Many VLC units use a halogen light, but there are some drawbacks
to this approach. First, the filament in a halogen light is heated to
a temperature of about $3000 \mathrm{K},$ which can cause heat degradation
of components in the curing unit itself. Second, less than 1$\%$ of the
energy given off by a halogen bulb is visible light, so a halogen bulb
must have a high power rating to produce the desired light intensity
at the wavelengths that CPQ will actually absorb.
More recently, VLC units have begun to use LEDs as their light
source. These lights stay cool, emit nearly all of their energy output
as visible light at the desired wavelength, and provide light with
an intensity as high as $1000 \mathrm{mW} / \mathrm{cm}^{2},$ which is about 10 times the intensity of sunlight on the surface of the Earth.

$\cdot$ What is the color of the light that is most effective at activating
the photoinitiator CPQ?
$$\begin{array}{ll}{\text { A. red }} & {\text { B. green }} \\ {\text { C. blue }} & {\text { D. ultraviolet }}\end{array}$$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:47

Problem 110

An essential part of modern dentistry is visible-light curing (VLC),
a procedure that hardens the restorative materials used in fillings, veneers, and other applications. These "curing lights" work
by activating molecules known as photoinitiators within the restorative materials. The photoinitiators, in turn, start a process of
polymerization that causes monomers to link together to form a
tough, solid polymer network. Thus, with VLC a dentist can apply
and shape soft restorative materials as desired, shine a bright light
on the result as shown in FIGURE $25-50(a),$ and in 20 seconds have a
completely hardened - or cured- final product.
The most common photoinitiator is camphoroquinone (CPQ).
To cure CPQ in the least time, one should illuminate it with light
having a wavelength that matches the wavelength at which CPQ
absorbs the most light. A rough plot of the relative absorption of
CPQ for light of different wavelengths is shown in FIGURE $25-50$ (b).
Many VLC units use a halogen light, but there are some drawbacks
to this approach. First, the filament in a halogen light is heated to
a temperature of about $3000 \mathrm{K},$ which can cause heat degradation
of components in the curing unit itself. Second, less than 1$\%$ of the
energy given off by a halogen bulb is visible light, so a halogen bulb
must have a high power rating to produce the desired light intensity
at the wavelengths that CPQ will actually absorb.
More recently, VLC units have begun to use LEDs as their light
source. These lights stay cool, emit nearly all of their energy output
as visible light at the desired wavelength, and provide light with
an intensity as high as $1000 \mathrm{mW} / \mathrm{cm}^{2},$ which is about 10 times the intensity of sunlight on the surface of the Earth.

$\cdot$ Suppose a VLC unit uses an LED that produces light with an
average intensity of 400 $\mathrm{mW} / \mathrm{cm}^{2} .$ What is the rms value of the
electric field in this beam of light?
$$\begin{array}{ll}{\text { A. } 1230 \mathrm{N} / \mathrm{C}} & {\text { B. } 390 \mathrm{N} / \mathrm{C}} \\ {\text { C. } 1700 \mathrm{N} / \mathrm{C}} & {\text { D. } 2.1 \times 10^{5} \mathrm{N} / \mathrm{C}}\end{array}$$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:16

Problem 111

An essential part of modern dentistry is visible-light curing (VLC),
a procedure that hardens the restorative materials used in fillings, veneers, and other applications. These "curing lights" work
by activating molecules known as photoinitiators within the restorative materials. The photoinitiators, in turn, start a process of
polymerization that causes monomers to link together to form a
tough, solid polymer network. Thus, with VLC a dentist can apply
and shape soft restorative materials as desired, shine a bright light
on the result as shown in FIGURE $25-50(a),$ and in 20 seconds have a
completely hardened - or cured- final product.
The most common photoinitiator is camphoroquinone (CPQ).
To cure CPQ in the least time, one should illuminate it with light
having a wavelength that matches the wavelength at which CPQ
absorbs the most light. A rough plot of the relative absorption of
CPQ for light of different wavelengths is shown in FIGURE $25-50$ (b).
Many VLC units use a halogen light, but there are some drawbacks
to this approach. First, the filament in a halogen light is heated to
a temperature of about $3000 \mathrm{K},$ which can cause heat degradation
of components in the curing unit itself. Second, less than 1$\%$ of the
energy given off by a halogen bulb is visible light, so a halogen bulb
must have a high power rating to produce the desired light intensity
at the wavelengths that CPQ will actually absorb.
More recently, VLC units have begun to use LEDs as their light
source. These lights stay cool, emit nearly all of their energy output
as visible light at the desired wavelength, and provide light with
an intensity as high as $1000 \mathrm{mW} / \mathrm{cm}^{2},$ which is about 10 times the intensity of sunlight on the surface of the Earth.

$\cdot$ How much radiation pressure does the beam of light in Problem
110 exert on a tooth, assuming the tooth absorbs all the light?
$$\begin{array}{ll}{\text { A. } 6.67 \times 10^{-8} \mathrm{N} / \mathrm{m}^{2}} & {\text { B. } 2.00 \times 10^{-6} \mathrm{N} / \mathrm{m}^{2}} \\ {\text { C. } 1.33 \times 10^{-5} \mathrm{N} / \mathrm{m}^{2}} & {\text { D. } 4.00 \times 10^{3} \mathrm{N} / \mathrm{m}^{2}}\end{array}$$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:24

Problem 112

An essential part of modern dentistry is visible-light curing (VLC),
a procedure that hardens the restorative materials used in fillings, veneers, and other applications. These "curing lights" work
by activating molecules known as photoinitiators within the restorative materials. The photoinitiators, in turn, start a process of
polymerization that causes monomers to link together to form a
tough, solid polymer network. Thus, with VLC a dentist can apply
and shape soft restorative materials as desired, shine a bright light
on the result as shown in FIGURE $25-50(a),$ and in 20 seconds have a
completely hardened - or cured- final product.
The most common photoinitiator is camphoroquinone (CPQ).
To cure CPQ in the least time, one should illuminate it with light
having a wavelength that matches the wavelength at which CPQ
absorbs the most light. A rough plot of the relative absorption of
CPQ for light of different wavelengths is shown in FIGURE $25-50$ (b).
Many VLC units use a halogen light, but there are some drawbacks
to this approach. First, the filament in a halogen light is heated to
a temperature of about $3000 \mathrm{K},$ which can cause heat degradation
of components in the curing unit itself. Second, less than 1$\%$ of the
energy given off by a halogen bulb is visible light, so a halogen bulb
must have a high power rating to produce the desired light intensity
at the wavelengths that CPQ will actually absorb.
More recently, VLC units have begun to use LEDs as their light
source. These lights stay cool, emit nearly all of their energy output
as visible light at the desired wavelength, and provide light with
an intensity as high as $1000 \mathrm{mW} / \mathrm{cm}^{2},$ which is about 10 times the intensity of sunlight on the surface of the Earth.

$\cdot$ Assuming the light from the VLC unit has a beam 0.50 $\mathrm{cm}$ in
diameter, how much energy does the light deliver in 20 seconds?
$$\begin{array}{ll}{\text { A. } 0.025 \mathrm{J}} & {\text { B. } 3.9 \mathrm{J}} \\ {\text { C. } 63 \mathrm{J}} & {\text { D. } 5000 \mathrm{J}}\end{array}$$

Nathan Silvano
Nathan Silvano
Numerade Educator
04:31

Problem 113

$\because$ Predict/Calculate REFERRING TO EXAMPLE $25-12$ Suppose the incident beam of light is linearly polarized in the same direction $\theta$
as the transmission axis of the analyzer. The transmission axis
of the polarizer remains vertical. (a) What value must $\theta$ have if
the transmitted intensity is to be 0.200$I_{0} ?$ (b) If $\theta$ is increased
from the value found in part (a), does the transmitted intensity
increase, decrease, or stay the same? Explain.

Nathan Silvano
Nathan Silvano
Numerade Educator
01:06

Problem 114

$. .$ REFERRING TO EXAMPLE $25-12$ Suppose the incident beam of light is
linearly polarized in the vertical direction. In addition, the transmission axis of the analyzer is at an angle of $80.0^{\circ}$ to the vertical.
What angle should the transmission axis of the polarizer make
with the vertical if the transmitted intensity is to be a maximum?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator