College Physics

Hugh D. Young Philip W. Adams

Chapter 23

Electromagnetic Waves - all with Video Answers

Educators

Chapter Questions

Problem 1

When a solar flare erupts on the surface of the sun, how many minutes after it occurs does its light show up in an astronomer's telescope on earth? (Consult Appendix E.)

Ze-Han Lee

Ze-Han Lee

Numerade Educator

Problem 2

The microprocessor in a modern laptop computer runs on a 2.5 GHz clock. Assuming that the electrical signals in the computer travel at two-thirds of the speed of light, how far does a signal travel in one clock cycle?

Prabhu Ramji

Numerade Educator

Problem 3

(a) How much time does it take light to travel from the moon to the earth, a distance of $384,000 \mathrm{~km} ?$ (b) Light from the star Sirius takes 8.61 years to reach the earth. What is the distance to Sirius in kilometers?

Ze-Han Lee

Numerade Educator

Problem 4

A geostationary communications satellite orbits the earth directly above the equator at an altitude of $35,800 \mathrm{~km}$. Calculate the time it would take a cell phone signal to travel from a point on the equator to the satellite and back. Would this delay be noticeable in a conversation?

Prabhu Ramji

Numerade Educator

Problem 5

Consider electromagnetic waves propagating in air. (a) Determine the frequency of a wave with a wavelength of (i) $5.0 \mathrm{~km},$ (ii) $5.0 \mu \mathrm{m}$,
(iii) $5.0 \mathrm{nm}$. (b) What is the wavelength (in meters and nanometers) of (i) gamma rays of frequency $6.50 \times 10^{21} \mathrm{~Hz}$, (ii) an AM station radio wave of frequency $590 \mathrm{kHz} ?$

Ze-Han Lee

Numerade Educator

Problem 6

Most people perceive light having a wavelength between $630 \mathrm{nm}$ and $700 \mathrm{nm}$ as red and light with a wavelength between $400 \mathrm{nm}$ and $440 \mathrm{nm}$ as violet. Calculate the approximate frequency ranges for
(a) violet light and (b) red light.

Ryan Hood

Numerade Educator

Problem 7

The electric field of a sinusoidal electromagnetic wave obeys the equation $E=-(375 \mathrm{~V} / \mathrm{m}) \sin \left[\left(5.97 \times 10^{15} \mathrm{rad} / \mathrm{s}\right) t+(1.99 \times\right.$
$\left.\left.10^{7} \mathrm{rad} / \mathrm{m}\right) x\right] .$ (a) What are the amplitudes of the electric and magnetic fields of this wave? (b) What are the frequency, wavelength, and period of the wave? Is this light visible to humans? (c) What is the speed of the wave?

Ze-Han Lee

Numerade Educator

Problem 8

A sinusoidal electromagnetic wave having a magnetic field of amplitude $1.25 \mu \mathrm{T}$ and a wavelength of $432 \mathrm{nm}$ is traveling in the $+x$ direction through empty space. (a) What is the frequency of this wave? (b) What is the amplitude of the associated electric field? (c) Write the equations for the electric and magnetic fields as functions of $x$ and $t$ in the form of Equations 23.3 .

Ryan Hood

Numerade Educator

Problem 9

The wavelength of visible light ranges from $400 \mathrm{nm}$ to $700 \mathrm{nm}$. Find the corresponding ranges of this light's (a) frequency, (b) angular frequency, (c) wave number.

Ze-Han Lee

Numerade Educator

Problem 10

There are two categories of ultraviolet light. Ultraviolet A (UVA) has a wavelength ranging from $320 \mathrm{nm}$ to $400 \mathrm{nm}$. It is not so harmful to the skin and is necessary for the production of vitamin D. UVB, with a wavelength between $280 \mathrm{nm}$ and $320 \mathrm{nm},$ is much more dangerous because it causes skin cancer.
(a) Find the frequency ranges of UVA and UVB.
(b) What are the ranges of the wave numbers for UVA and UVB?

Prabhu Ramji

Numerade Educator

Problem 11

Medical X-rays are taken with electromagnetic waves having a wavelength around $0.10 \mathrm{nm}$. What are the frequency, period, and wave number of such waves?

Prabhu Ramji

Numerade Educator

Problem 12

A radio broadcasts at a wavelength of $3.06 \mathrm{~m}$. Near the broadcast tower the electric-field amplitude is $2700 \mathrm{~N} / \mathrm{C}$. Calculate (a) the frequency, (b) the wave number, and (c) the magnetic-field amplitude of the electromagnetic wave.

Prabhu Ramji

Numerade Educator

Problem 13

A sinusoidal electromagnetic wave of frequency $6.10 \times 10^{14} \mathrm{~Hz}$ travels in vacuum in the $+x$ direction. The magnetic field is parallel to the $y$ axis and has amplitude $5.80 \times 10^{-4} \mathrm{~T}$. (a) Find the magnitude and direction of the electric field. (b) Write the wave functions for the electric and magnetic fields in the form of Equations $23.3 .$

Prabhu Ramji

Numerade Educator

Problem 14

Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of the wave? (a) $\vec{E}$ in the $+x$ direction, $\vec{B}$ in the $+y$ direction (b) $\vec{E}$ in the $-y$ direction, $\vec{B}$ in the $+x$ direction (c) $\vec{E}$ in the $+z$ direction, $\vec{B}$ in the $-x$ direction (d) $\vec{E}$ in the $+y$ direction, $\vec{B}$ in the $-z$ direction

Ryan Hood

Numerade Educator

Problem 15

Write the wave equation for the electric field of an electromagnetic wave that is traveling in the $+x$ direction with a wavelength of $2.0 \mathrm{~m}$ and an amplitude of $100 \mathrm{~N} / \mathrm{C}$. Give the wave equation in terms of its angular frequency and wave number.

Prabhu Ramji

Numerade Educator

Problem 16

He-Ne lasers are often used in physics demonstrations. They produce light of wavelength $633 \mathrm{nm}$ and a power of $0.500 \mathrm{~mW}$ spread over a cylindrical beam $1.00 \mathrm{~mm}$ in diameter (although these quantities can vary). (a) What is the intensity of this laser beam?
(b) What are the maximum values of the electric and magnetic fields? (c) What is the average energy density in the laser beam?

Ze-Han Lee

Numerade Educator

Problem 17

We can reasonably model a $75 \mathrm{~W}$ incandescent lightbulb as a sphere $6.0 \mathrm{~cm}$ in diameter. Typically, only about $5 \%$ of the energy goes to visible light; the rest goes largely to nonvisible infrared radiation. (a) What is the visible light intensity (in $\mathrm{W} / \mathrm{m}^{2}$ ) at the surface of the bulb? (b) What are the amplitudes of the electric and magnetic fields at this surface, for a sinusoidal wave with this intensity?

Ze-Han Lee

Numerade Educator

Problem 18

Scientists are working on a new technique to kill cancer cells by zapping them with ultrahighenergy (in the range of $10^{12} \mathrm{~W}$ ) pulses of electromagnetic waves that last for an extremely short time (a few nanoseconds). These short pulses scramble the interior of a cell without causing it to explode, as long pulses would do. We can model a typical such cell as a disk $5.0 \mu \mathrm{m}$ in diameter, with the pulse lasting for $4.0 \mathrm{~ns}$ with an average power of $2.0 \times 10^{12} \mathrm{~W}$. We shall assume that the energy is spread uniformly over the faces of 100 cells for each pulse. (a) How much energy is given to the cell during this pulse? (b) What is the intensity (in $\mathrm{W} / \mathrm{m}^{2}$ ) delivered to the cell? (c) What are the maximum values of the electric and magnetic fields in the pulse?

Prabhu Ramji

Numerade Educator

Problem 19

At the floor of a room, the intensity of light from bright overhead lights is $8.00 \mathrm{~W} / \mathrm{m}^{2} .$ Find the radiation pressure on a totally absorbing section of the floor.

Ryan Hood

Numerade Educator

Problem 20

The intensity at a certain distance from a bright light source is $6.00 \mathrm{~W} / \mathrm{m}^{2} .$ Find the radiation pressure (in pascals and in atmospheres) on (a) a totally absorbing surface and (b) a totally reflecting surface.

Ze-Han Lee

Numerade Educator

Problem 21

A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area $0.500 \mathrm{~m}^{2}$. At the window, the electric field of the wave has rms value $0.0200 \mathrm{~V} / \mathrm{m} .$ How much energy does this wave carry through the window during a 30.0 s commercial?

Prabhu Ramji

Numerade Educator

Problem 22

A sinusoidal electromagnetic wave has an average intensity of $100 \mathrm{~W} / \mathrm{m}^{2} .$ By what factor would the electric-field amplitude of the wave have to be increased in order for the wave to have an average intensity of $10,000 \mathrm{~W} / \mathrm{m}^{2} ?$

Prabhu Ramji

Numerade Educator

Problem 23

Radiation falling on a perfectly reflecting surface produces an average pressure $p .$ If radiation of the same intensity falls on a perfectly absorbing surface and is spread over twice the area, what is the pressure at that surface in terms of $p ?$

Prabhu Ramji

Numerade Educator

Problem 24

A sinusoidal electromagnetic wave emitted by a cellular phone has a wavelength of $35.4 \mathrm{~cm}$ and an electric-field amplitude of $5.40 \times 10^{-2} \mathrm{~V} / \mathrm{m}$ at a distance of $250 \mathrm{~m}$ from the antenna. Calculate (a) the frequency of the wave; (b) the magnetic-field amplitude; (c) the intensity of the wave.

Prabhu Ramji

Numerade Educator

Problem 25

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point $11.5 \mathrm{~cm}$ from their point of intersection, as shown in Figure $23.47 .$ For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is $28.0 \mathrm{~cm}$ long) after reflecting from the first mirror?

Ryan Hood

Numerade Educator

Problem 26

I Two plane mirrors $A$ and $B$ intersect at a $45^{\circ}$ angle. Three rays of light leave point $P$ (see Figure 23.48 ) and strike one of the mirrors. What is the subsequent path of each of the following rays until they no longer strike either of the mirrors?
(a) Ray $1,$ which strikes $A$ at $45^{\circ}$ with respect to the normal
(b) Ray $2,$ which strikes $B$ traveling perpendicular to mirror $A$
(c) Ray $3,$ which strikes $B$ perpendicular to its surface

Prabhu Ramji

Numerade Educator

Problem 27

? Prove that when a ray of light travels at any angle into the corner formed by two mirrors placed at right angles to each other, the reflected ray emerges parallel to the original ray (see Figure 23.49 ).

Shoukat Ali

Other Schools

Problem 28

A light beam travels at $1.94 \times 10^{8} \mathrm{~m} / \mathrm{s}$ in quartz. The wavelength of the light in quartz is $355 \mathrm{nm}$. (a) What is the index of refraction of quartz at this wavelength? (b) If this same light travels through air, what is its wavelength there?

Ryan Hood

Numerade Educator

Problem 29

Using a fast-pulsed laser and electronic timing circuitry, you find that light takes 0.20 ns longer to travel down a zircon rod of length $L$ than to travel the same distance in air. What is the length of the zircon rod?

Prabhu Ramji

Numerade Educator

Problem 30

Light with a frequency of $5.80 \times 10^{14} \mathrm{~Hz}$ travels in a block of glass that has an index of refraction of $1.52 .$ What is the wavelength of the light (a) in vacuum and (b) in the glass?

Mohit Khurana

Texas A&M University

Problem 31

The speed of light with a wavelength of $656 \mathrm{nm}$ in heavy flint glass is $1.82 \times 10^{8} \mathrm{~m} / \mathrm{s}$. What is the index of refraction of the glass at this wavelength?

Shoukat Ali

Other Schools

Problem 32

The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of $1.34 .$ Visible light ranges in wavelength from $400 \mathrm{nm}$ (violet) to $700 \mathrm{nm}$ (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

Prabhu Ramji

Numerade Educator

Problem 33

Light of a certain frequency has a wavelength of $438 \mathrm{nm}$ in water. What is the wavelength of this light (a) in benzene, (b) in air? (See Table $23.1 .)$

Prabhu Ramji

Numerade Educator

Problem 34

II A 1.55-m-tall fisherman stands at the edge of a lake, being watched by a suspicious trout that is $3.50 \mathrm{~m}$ from the fisherman in the horizontal direction and $45.0 \mathrm{~cm}$ below the surface of the water. At what angle from the vertical does the fish see the top of the fisherman's head?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 35

A light ray passes through a rectangular slab of transparent material having index of refraction $n=2,$ as shown in Figure $23.50 .$ The incident angle is $\theta_{0}=60.0^{\circ} .$ Determine (a) $\theta_{a}$
(b) $\theta_{b}$, and (c) $\theta_{c}$. (d) What is the relationship between the directions of the incident ray and the emerging ray?

Prabhu Ramji

Numerade Educator

Problem 36

A glass plate having parallel faces and a refractive index of 1.58 lies at the bottom of a liquid of refractive index $1.70 .$ A ray of light in the liquid strikes the top of the glass at an angle of incidence of $62.0^{\circ} .$ Compute the angle of refraction of this light in the glass.

Ryan Hood

Numerade Educator

Problem 37

A beam of light in air makes an angle of $47.5^{\circ}$ with the surface (not the normal) of a glass plate having a refractive index of 1.66 .
(a) What is the angle between the reflected part of the beam and the surface of the glass? (b) What is the angle between the refracted beam and the surface (not the normal) of the glass?

Shoukat Ali

Other Schools

Problem 38

Ray 1 of light in medium $a$ (see Figure 23.51 ) strikes the surface at $51.0^{\circ}$ with respect to the normal. (a) Find the angle of refraction of ray 1 with respect to the normal in medium $b$.
(b) Now repeat the problem with the light ray's direction reversed. The ray now approaches from below at the angle that you calculated in part (a). Find the angle of refraction in medium
a. (c) Do the refraction angles change when the ray is reversed?

Prabhu Ramji

Numerade Educator

Problem 39

You (height of your eyes above the water, $1.75 \mathrm{~m}$ ) are standing $2.00 \mathrm{~m}$ from the edge of a $2.50-\mathrm{m}$ -deep swimming pool (Figure 23.52 ). You notice that you can barely see your cell phone, which went missing a few minutes before, on the bottom of the pool. How far from the side of the pool is your cell phone?

Prabhu Ramji

Numerade Educator

Problem 40

A parallel-sided plate of glass having a refractive index of 1.60 is in contact with the surface of water in a tank. A ray coming from above makes an angle of incidence of $32.0^{\circ}$ with the normal to the top surface of the glass. What angle does this ray make with the normal in the water?

Prabhu Ramji

Numerade Educator

Problem 41

As shown in Figure $23.53,$ a layer of water covers a slab of material $X$ in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find
(a) the index of refraction of material $X$ and $(b)$ the angle the light makes with the normal in the air .

Salamat Ali

Numerade Educator

Problem 42

A ray of light in diamond (index of refraction 2.42 ) is incident on an interface with air. What is the largest angle the ray can make with the normal and not be totally reflected back into the diamond?

Shoukat Ali

Other Schools

Problem 43

The critical angle for total internal reflection at a liquid-air interface is $42.5^{\circ} .$ (a) If a ray of light traveling in the liquid has an angle of incidence of $35.0^{\circ}$ at the interface, what angle does the refracted ray in the air make with the normal? (b) If a ray of light traveling in air has an angle of incidence of $35.0^{\circ}$ at the interface, what angle does the refracted ray in the liquid make with the normal?

Ryan Hood

Numerade Educator

Problem 44

A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass-water interface at an angle to the normal greater than $48.7^{\circ},$ no light is refracted into the water. What is the refractive index of the glass?

Prabhu Ramji

Numerade Educator

Problem 45

Light is incident along the normal to face $A B$ of a prism that has a refractive index $n$ and an angle $\alpha=30^{\circ}$, as shown in Figure $23.54 .$ When the prism is in air, the light undergoes total internal reflection. However, when the prism is immersed in water, a faint refracted ray emerges at an angle of $80^{\circ}$ to the normal of face $A C$. (a) Determine $n$. (b) What material was used to make the prism?

Prabhu Ramji

Numerade Educator

Problem 46

Light enters a solid tube made of plastic having an index of refraction of $1.60 .$ The light travels parallel to the upper part of the tube. (See Figure $23.55 .)$ You want to cut the face $A B$ so that all the light will reflect back into the tube after it first strikes that face.
(a) What is the largest that $\theta$ can be if the tube is in air? (b) If the tube is immersed in water of refractive index $1.33,$ what is the largest that $\theta$ can be?

Prabhu Ramji

Numerade Educator

Problem 47

An optical fiber consists of an outer "cladding" layer and an inner core with a slightly higher index of refraction. Light rays entering the core are trapped inside by total internal reflection and forced to travel along the fiber (see Figure 23.56 ). Suppose the cladding has an index of refraction of $n_{b}=1.44$ and the core has an index of refraction of $n_{a}=1.46 .$ Calculate the largest angle $\theta$ between a light ray and the longitudinal axis of the fiber (see the figure) for which the ray will be totally internally reflected at the core/cladding boundary.

Prabhu Ramji

Numerade Educator

Problem 48

A beam of light strikes a sheet of glass at an angle of $57.0^{\circ}$ with the normal in air. You observe that red light makes an angle of $38.1^{\circ}$ with the normal in the glass, while violet light makes a $36.7^{\circ}$ angle.
(a) What are the indices of refraction of this glass for these colors of light? (b) What are the speeds of red and violet light in the glass?

Prabhu Ramji

Numerade Educator

Problem 49

The table gives the index of refraction of fused silica glass as a function of wavelength (in vacuum).
$$
\begin{array}{cl}
\hline \text { Wavelength (nm) } & n \\
\hline 230 & 1.5202 \\
400 & 1.4701 \\
600 & 1.4580 \\
800 & 1.4533 \\
1300 & 1.4469 \\
1600 & 1.4434 \\
2200 & 1.4350 \\
\hline
\end{array}
$$
Construct a graph of the index of refraction as a function of the wavelength. Make a "best fit" to the linear portion of the data curve to determine at what wavelength $n=1.4200$. To what portion of the electromagnetic spectrum does this wavelength correspond (see Figure 23.3 )?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 50

Use the graph in Figure 23.29 for silicate flint glass. (a) What are the indices of refraction of this glass for extreme violet light of wavelength $400 \mathrm{nm}$ and for extreme red light of wavelength $700 \mathrm{nm} ?$ (b) What are the wavelengths of $400 \mathrm{nm}$ violet light and $700 \mathrm{nm}$ red light in this glass?
(c) Calculate the ratio of the speed of extreme red light to that of extreme violet light in the glass. Which of these travels faster in the glass? (d) If a beam of white light in air strikes a sheet of this glass at $65.0^{\circ}$ with the normal in air, what will be the angle of dispersion between the extremes of visible light in the glass? In other words, what will be the angle between extreme red and extreme violet light in the glass?

Shoukat Ali

Other Schools

Problem 51

The indices of refraction for violet light $(\lambda=400 \mathrm{nm})$ and red light $(\lambda=700 \mathrm{nm})$ in diamond are 2.46 and $2.41,$ respectively. A ray of light traveling through air strikes the diamond surface at an angle of $53.5^{\circ}$ to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

Ryan Hood

Numerade Educator

Problem 52

Unpolarized light with intensity $I_{0}$ is incident on an ideal polarizing filter. The emerging light strikes a second ideal polarizing filter whose axis is at $41.0^{\circ}$ to that of the first. Determine (a) the intensity of the beam after it has passed through the second polarizer and (b) its state of polarization.

Shoukat Ali

Other Schools

Problem 53

Unpolarized light is incident on two ideal polarizing filters. The second filter's axis is rotated through an angle $\theta$ relative to that of the first filter. If the intensity of light emerging from the second filter is $1 / 10$ the intensity of the incident light, what is $\theta ?$

Prabhu Ramji

Numerade Educator

Problem 54

A beam of unpolarized light of intensity $I_{0}$ passes through a series of ideal polarizing filters with their polarizing directions turned to different angles as shown in Figure 23.57 . (a) What is the light intensity (in terms of $I_{0}$ ) at points $A, B,$ and $C ?$ (b) If we remove the middle filter, what will be the light intensity at point $C ?$

Prabhu Ramji

Numerade Educator

Problem 55

Three ideal polarizing filters are stacked, with the polarizing axes of the second and third filters at $23.0^{\circ}$ and $62.0^{\circ},$ respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity $75.0 \mathrm{~W} / \mathrm{cm}^{2}$ after it passes through the stack. If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

Prabhu Ramji

Numerade Educator

Problem 56

Light of original intensity $I_{0}$ passes through two ideal polarizing filters having their polarizing axes oriented as shown in Figure $23.58 .$ You want to adjust the angle $\phi$ so that the intensity at point $P$ is equal to $I_{0} / 10 .$ (a) If the original light is unpolarized, what should $\phi$ be? (b) If the original light is linearly polarized in the same direction as the polarizing axis of the first polarizer the light reaches, what should $\phi$ be?

Shoukat Ali

Other Schools

Problem 57

The polarizing angle for light in air incident on a glass plate is $57.6^{\circ} .$ What is the index of refraction of the glass?

Ryan Hood

Numerade Educator

Problem 58

A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is $30^{\circ}$, the intensity of the emerging beam is $I$. If you instead want the intensity to be $I / 2,$ what should be the angle between the filter axis and the original direction of polarization of the light?

Prabhu Ramji

Numerade Educator

Problem 59

A beam of unpolarized light in air is incident at an angle of $54.5^{\circ}$ (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized.
(a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam?

Prabhu Ramji

Numerade Educator

Problem 60

Plane-polarized light passes through two polarizers whose axes are oriented at $35.0^{\circ}$ to each other. If the intensity of the original beam is reduced to $15.0 \%,$ what was the polarization direction of the original beam, relative to the first polarizer?

Prabhu Ramji

Numerade Educator

Problem 61

The energy flow to the earth from sunlight is about $1.4 \mathrm{~kW} / \mathrm{m}^{2}$.
(a) Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity. (b) The distance from the earth to the sun is about $1.5 \times 10^{11} \mathrm{~m}$. Find the total power radiated by the sun.

Mohit Khurana

Texas A&M University

Problem 62

A plane sinusoidal electromagnetic wave in air has a wavelength of $3.84 \mathrm{~cm}$ and an $\vec{E}$ -field amplitude of $1.35 \mathrm{~V} / \mathrm{m}$. (a) What is the frequency of the wave? (b) What is the $\vec{B}$ -field amplitude? (c) What is the intensity? (d) What average force does this radiation exert perpendicular to its direction of propagation on a totally absorbing surface with area $0.240 \mathrm{~m}^{2} ?$

Prabhu Ramji

Numerade Educator

Problem 63

A powerful searchlight shines on a man. The man's cross-sectional area is $0.500 \mathrm{~m}^{2}$ perpendicular to the light beam, and the intensity of the light at his location is $36.0 \mathrm{~kW} / \mathrm{m}^{2}$. He is wearing black clothing, so that the light incident on him is totally absorbed. What is the magnitude of the force the light beam exerts on the man? Do you think he could sense this force?

Prabhu Ramji

Numerade Educator

Problem 64

Laser surgery. Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portion back into place. In one such procedure, a laser beam has a wavelength of $810 \mathrm{nm}$ and delivers $250 \mathrm{~mW}$ of power spread over a circular spot $510 \mu \mathrm{m}$ in diameter. The vitreous humor (the transparent fluid that fills most of the eye) has an index of refraction of $1.34 .$ (a) If the laser pulses are each $1.50 \mathrm{~ms}$ long, how much energy is delivered to the retina with each pulse?
(b) What average pressure does the pulse of the laser beam exert on the retina as it is fully absorbed by the circular spot? (c) What are the wavelength and frequency of the laser light inside the vitreous humor of the eye? (d) What are the maximum values of the electric and magnetic fields in the laser beam?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 65

A small helium-neon laser emits red visible light with a power of $3.20 \mathrm{~mW}$ in a beam that has a diameter of $2.50 \mathrm{~mm}$. (a) What are the amplitudes of the electric and magnetic fields of the light? (b) What are the average energy densities associated with the electric field and with the magnetic field? (c) What is the total energy contained in a $1.00 \mathrm{~m}$ length of the beam?

Laszlo Zalavari

Laszlo Zalavari

Numerade Educator

Problem 66

Radio receivers can comfortably pick up a broadcasting station's signal when the electric-field strength of the signal is about $10.0 \mathrm{mV} / \mathrm{m} .$ If a radio station broadcasts in all directions with an average power of $50.0 \mathrm{~kW},$ what would be the maximum distance at which you could easily pick up its transmissions? (Atmospheric conditions can have major effects on this distance.)

Prabhu Ramji

Numerade Educator

Problem 67

NASA is doing research on the concept of solar sailing. A solar sailing craft uses a large, low-mass sail and the energy and momentum of sunlight for propulsion. (a) Should the sail be absorptive or reflective? Why? (b) The total power output of the sun is $3.9 \times 10^{26} \mathrm{~W} .$ How large a sail is necessary to propel a $10,000 \mathrm{~kg}$ spacecraft against the gravitational force of the sun? Express your result in square kilometers. (c) Explain why your answer to part (b) is independent of the distance from the sun.

Prabhu Ramji

Numerade Educator

Problem 68

A thick layer of oil is floating on the surface of water in a tank. A beam of light traveling in the oil is incident on the water interface at an angle of $30.0^{\circ}$ from the normal. The refracted beam travels in the water at an angle of $45.0^{\circ}$ from the normal. What is the refractive index of the oil?

Prabhu Ramji

Numerade Educator

Problem 69

You want to support a sheet of fireproof paper horizontally, using only a vertical upward beam of light spread uniformly over the sheet. There is no other light on this paper. The sheet measures $22.0 \mathrm{~cm}$ by $28.0 \mathrm{~cm}$ and has a mass of $1.50 \mathrm{~g}$. (a) If the paper is black and hence absorbs all the light that hits it, what must be the intensity of the light beam? (b) For the light in part (a), what are the maximum values of its electric and magnetic fields? (c) If the paper is white and hence reflects all the light that hits it, what intensity of light beam is needed to support it?
(d) To see if it is physically reasonable to expect to support a sheet of paper this way, calculate the intensity in a typical $0.500 \mathrm{~mW}$ laser beam that is $1.00 \mathrm{~mm}$ in diameter and compare this value with your answer in part (a).

Prabhu Ramji

Numerade Educator

Problem 70

A light ray in air strikes the right-angle prism shown in Figure $23.59 .$ This ray consists of two different wavelengths. When it emerges at face $A B,$ it has been split into two different rays that diverge from each other by $8.50^{\circ} .$ Find the index of refraction of the prism for each of the two wavelengths.

Mayukh Banik

Numerade Educator

Problem 71

A ray of light is incident in air on a block of a transparent solid whose index of refraction is $n .$ If $n=1.38,$ what is the largest angle of incidence, $\theta_{a},$ for which total internal reflection will occur at the vertical face (point $A$ shown in Figure 23.60 )?

Salamat Ali

Numerade Educator

Problem 72

A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, it takes the light 8.72 ns to travel the length of the tube, but when the tube is filled with a transparent jelly, it takes the light 2.04 ns longer to travel its length. What is the refractive index of this jelly?

Shoukat Ali

Other Schools

Problem 73

Physicians use high-frequency $(f=1 \mathrm{MHz}$ to $5 \mathrm{MHz}$ ) sound waves, called ultrasound, to image internal organs. The speed of these ultrasound waves is $1480 \mathrm{~m} / \mathrm{s}$ in muscle and $344 \mathrm{~m} / \mathrm{s}$ in air. We define the index of refraction of a material for sound waves
to be the ratio of the speed of sound in air to the speed of sound in the material. Snell's law then applies to the refraction of sound waves. (a) At what angle from the normal does an ultrasound beam enter the heart if it leaves the lungs at an angle of $9.73^{\circ}$ from the normal to the heart wall? (Assume that the speed of sound in the lungs is $344 \mathrm{~m} / \mathrm{s} .)$ (b) What is the critical angle for sound waves in air incident on muscle?

Dading Chen

Numerade Educator

Problem 74

A light ray refracts through a glass block having a thickness $t$ and index of refraction $1.5 .$ As shown in Figure 23.61 , the exiting ray is displaced from the incident ray by $y=0.2 \mathrm{~cm} .$ What is the thickness $t$ of the glass block?

Prabhu Ramji

Numerade Educator

Problem 75

A beaker with a mirrored bottom is filled with a liquid whose index of refraction is 1.63. A light beam strikes the top surface of the liquid at an angle of $42.5^{\circ}$ from the normal. At what angle from the normal will the beam exit from the liquid after traveling down through it, reflecting from the mirrored bottom, and returning to the surface?

Mayukh Banik

Numerade Educator

Problem 76

A ray of light traveling in a block of glass $(n=1.52)$ is incident on the top surface at an angle of $57.2^{\circ}$ with respect to the normal in the glass. If a layer of oil is placed on the top surface of the glass, the ray is totally reflected. What is the maximum possible index of refraction of the oil?

Salamat Ali

Numerade Educator

Problem 77

In a physics lab, light with wavelength $490 \mathrm{nm}$ travels in air from a laser to a photocell in $17.0 \mathrm{~ns}$. When a slab of glass $0.840 \mathrm{~m}$ thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light $21.2 \mathrm{~ns}$ to travel from the laser to the photocell. What is the wavelength of the light in the glass?

Ryan Hood

Numerade Educator

Problem 78

The refractive index of a certain glass is $1.66 .$ For what angle of incidence is light that is reflected from the surface of this glass completely polarized if the glass is immersed in (a) air or (b) water?

Ryan Hood

Numerade Educator

Problem 79

A thin layer of ice $(n=1.309)$ floats on the surface of water $(n=1.333)$ in a bucket. A ray of light from the bottom of the bucket travels upward through the water. (a) What is the largest angle with respect to the normal that the ray can make at the ice-water interface and still pass out into the air above the ice? (b) What is this angle after the ice melts?

Salamat Ali

Numerade Educator

Problem 80

Many biologically important molecules are optically active. When linearly polarized light traverses a solution of compounds containing these molecules, its plane of polarization is rotated. Some compounds rotate the polarization clockwise; others rotate the polarization counterclockwise. The amount of rotation depends on the amount of material in the path of the light. The following data give the amount of rotation through two amino acids over a path length of $100 \mathrm{~cm}$
From these data, find the relationship between the concentration $C$ (in grams per $100 \mathrm{~mL}$ ) and the rotation of the polarization (in degrees) of each amino acid. (Hint: Graph the concentration as a function of the rotation angle for each amino acid.)

Ryan Hood

Numerade Educator

Problem 81

There have been many studies of the effects on humans of electromagnetic waves of various frequencies. Using these studies, the International Commission on NonIonizing Radiation Protection (ICNIRP) produced guidelines for limiting exposure to electromagnetic fields, with the goal of protecting people against known adverse health effects. At frequencies of $1 \mathrm{~Hz}$ to $25 \mathrm{~Hz}$, the maximum exposure level of electric-field amplitude, $E_{\max },$ for the general public is $14 \mathrm{kV} / \mathrm{m}$. (Different guidelines were created for people who have occupational exposure to radiation.) At frequencies of $25 \mathrm{~Hz}$ to $3 \mathrm{kHz},$ the corresponding $E_{\max }$ is $\frac{350}{f} \mathrm{kV} / \mathrm{m},$ where $f$ is the frequency in $\mathrm{kHz}$.
In the United States, household electric power is provided at a frequency of $60 \mathrm{~Hz}$, so electromagnetic radiation at that frequency is of particular interest. On the basis of the ICNIRP guidelines, what is the maximum intensity of an electromagnetic wave at this frequency to which the general public should be exposed?
A. $7.7 \mathrm{~W} / \mathrm{m}^{2}$
B. $160 \mathrm{~W} / \mathrm{m}^{2}$
C. $45 \mathrm{~kW} / \mathrm{m}^{2}$
D. $260 \mathrm{~kW} / \mathrm{m}^{2}$

Prabhu Ramji

Numerade Educator

Problem 82

There have been many studies of the effects on humans of electromagnetic waves of various frequencies. Using these studies, the International Commission on NonIonizing Radiation Protection (ICNIRP) produced guidelines for limiting exposure to electromagnetic fields, with the goal of protecting people against known adverse health effects. At frequencies of $1 \mathrm{~Hz}$ to $25 \mathrm{~Hz}$, the maximum exposure level of electric-field amplitude, $E_{\max },$ for the general public is $14 \mathrm{kV} / \mathrm{m}$. (Different guidelines were created for people who have occupational exposure to radiation.) At frequencies of $25 \mathrm{~Hz}$ to $3 \mathrm{kHz},$ the corresponding $E_{\max }$ is $\frac{350}{f} \mathrm{kV} / \mathrm{m},$ where $f$ is the frequency in $\mathrm{kHz}$.
Doubling the frequency of a wave in the range of $25 \mathrm{~Hz}$ to $3 \mathrm{kHz}$ represents what change in the maximum allowed electromagneticwave intensity?
A. A factor of 2
B. A factor of $1 / \sqrt{2}$
C. A factor of $\frac{1}{2}$
D. A factor of $\frac{1}{4}$

Prabhu Ramji

Numerade Educator

Problem 83

There have been many studies of the effects on humans of electromagnetic waves of various frequencies. Using these studies, the International Commission on NonIonizing Radiation Protection (ICNIRP) produced guidelines for limiting exposure to electromagnetic fields, with the goal of protecting people against known adverse health effects. At frequencies of $1 \mathrm{~Hz}$ to $25 \mathrm{~Hz}$, the maximum exposure level of electric-field amplitude, $E_{\max },$ for the general public is $14 \mathrm{kV} / \mathrm{m}$. (Different guidelines were created for people who have occupational exposure to radiation.) At frequencies of $25 \mathrm{~Hz}$ to $3 \mathrm{kHz},$ the corresponding $E_{\max }$ is $\frac{350}{f} \mathrm{kV} / \mathrm{m},$ where $f$ is the frequency in $\mathrm{kHz}$.
The ICNIRP also has guidelines for magnetic-field exposure for the general public. In the frequency range of $25 \mathrm{~Hz}$ to $3 \mathrm{kHz},$ this guideline states that the maximum allowed magnetic-field amplitude is $5 / f \mathrm{~T},$ where $f$ is the frequency in $\mathrm{kHz}$. Which is a more stringent limit on allowable electromagnetic-wave intensity in this frequency range: the electric-field guideline or the magnetic-field guideline?
A. The magnetic-field guideline, because at a given frequency the allowed magnetic field is smaller than the allowed electric field.
B. The electric-field guideline, because at a given frequency the allowed intensity calculated from the electric-field guideline is smaller.
C. It depends on the particular frequency chosen (both guidelines are frequency dependent).
D. Neither-for any given frequency, the guidelines represent the same electromagnetic-wave intensity.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 84

Some insect eyes have two types of cells that are sensitive to the plane of polarization of light. In a simple model, one cell type (type $\mathrm{H}$ ) is sensitive to horizontally polarized light only, and the other cell type (type $\mathrm{V}$ ) is sensitive to vertically polarized light only. To study the responses of these cells, researchers fix the insect in a normal, upright position so that one eye is illuminated by a light source. Then several experiments are carried out.
First, light with a plane of polarization at $45^{\circ}$ to the horizontal shines on the insect. Which statement is true about the two types of cells?
A. Both types detect this light.
B. Neither type detects this light.
C. Only type $\mathrm{H}$ detects the light.
D. Only type $\mathrm{V}$ detects the light.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 85

Some insect eyes have two types of cells that are sensitive to the plane of polarization of light. In a simple model, one cell type (type $\mathrm{H}$ ) is sensitive to horizontally polarized light only, and the other cell type (type $\mathrm{V}$ ) is sensitive to vertically polarized light only. To study the responses of these cells, researchers fix the insect in a normal, upright position so that one eye is illuminated by a light source. Then several experiments are carried out.
Next, unpolarized light is reflected off a smooth horizontal piece of glass, and the reflected light shines on the insect. Which statement is true about the two types of cells?
A. When the light is directly above the glass, only type $\mathrm{V}$ detects the reflected light.
B. When the light is directly above the glass, only type $\mathrm{H}$ detects the reflected light.
C. When the light is about $35^{\circ}$ above the horizontal, type $\mathrm{V}$ responds much more strongly than type $\mathrm{H}$ does.
D. When the light is about $35^{\circ}$ above the horizontal, type $\mathrm{H}$ responds much more strongly than type $\mathrm{V}$ does.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 86

Some insect eyes have two types of cells that are sensitive to the plane of polarization of light. In a simple model, one cell type (type $\mathrm{H}$ ) is sensitive to horizontally polarized light only, and the other cell type (type $\mathrm{V}$ ) is sensitive to vertically polarized light only. To study the responses of these cells, researchers fix the insect in a normal, upright position so that one eye is illuminated by a light source. Then several experiments are carried out.
To vary the angle as well as the intensity of polarized light, ordinary unpolarized light is passed through one polarizer with its transmission axis vertical, and then a second polarizer is placed between the first polarizer and the insect. When the light leaving the second polarizer has half the intensity of the original unpolarized light, which statement is true about the two types of cells?
A. Only type H detects this light.
B. Only type $V$ detects this light.
C. Both types detect this light, but type $\mathrm{H}$ detects more light.
D. Both types detect this light, but type $\mathrm{V}$ detects more light.

Ummatul Choudary

Ummatul Choudary

Numerade Educator