Deck 22: Electromagnetic Waves

Question 1

$\varepsilon_{0} \mu_{0}=$ ?

A) $\mathrm{C}^{-2}$
B) $\mathrm{C}$
C) $\mathrm{c}^{2}$
D) $\mathrm{C}^{-1}$
E) $\mathrm{C}^{1 / 2}$

Answer 1

$\mathrm{C}^{-2}$

Question 2

How long does it take for a radio signal to travel to a spacecraft $1.5 \times 1011$ m away?

A) $1.0 \times 10^{3} \mathrm{~s}$
B) $5.0 \times 10^{2} \mathrm{~s}$
C) $5.0 \mathrm{~s}$
D) $5.0 \times 10^{3} \mathrm{~s}$
E) $50 \mathrm{~s}$

Answer 2

$5.0 \times 10^{2} \mathrm{~s}$

Question 3

What is a light-year in SI units?

A) $3.0 \times 1015 \mathrm{~m}$
B) $3.0 \times 1011 \mathrm{~m}$
C) $1.1 \times 10^{11} \mathrm{~m}$
D) $4.5 \times 1037 \mathrm{~m}$
E) $9.5 \times 1015 \mathrm{~m}$

Answer 3

$9.5 \times 1015 \mathrm{~m}$

Question 4

What is the speed of light in a material that has an index of refraction of 2.0?

A) $1.5 \times 10^{8} \mathrm{~m} / \mathrm{s}$
B) $2.0 \times 10^{8}\mathrm{~m} / \mathrm{s}$
C) $5.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$
D) $6.0 \times 10^{8} \mathrm{~m} / \mathrm{s}$
E) No such index can exist.

Question 5

Household wiring can emit electromagnetic waves of frequency $60 \mathrm{~Hz}$ . What is the wavelength of these waves?

A) $5.0 \times 10^{6} \mathrm{~m}$
B) $5.0 \times 10^{4} \mathrm{~m}$
C) $5.0 \times 10^{3} \mathrm{~m}$
D) $5.0 \times 10^{2} \mathrm{~m}$
E) $5.0 \times 10^{5} \mathrm{~m}$

Question 6

The Sun is $1.50 \times 10^{8} \mathrm{~km}$ from the Earth. How long does it take for light to reach us from the Sun?

A) $8.33 \mathrm{~min}$
B) $2.00 \mathrm{~s}$
C) $0.50 \mathrm{~s}$
D) $2.00 \mathrm{~ms}$
E) almost instantaneous

Question 7

What iindex of refraction halves the wavelength that light has in a vacuum?

A) 2.00
B) 1.33
C) 5.00
D) 1.41
E) 1.50

Question 8

Light passes from medium one ( $\left.\mathrm{v}_{1}\right)$ to medium two $\left(\mathrm{v}_{2}\right)$ . If $\mathrm{v}_{1}<\mathrm{v}_{2}$ then at the boundary

A) $f$ does not change, $\lambda$ increases.
B) $f$ increases, $\lambda$ decreases.
C) $f$ decreases, $\lambda$ increases.
D) $f$ does not change, $\lambda$ decreases.

Question 9

Which of the following is the direction of an electromagnetic wave having electric and magnetic field vectors $\mathbf{E}$ and $\mathbf{B}$ ?

A) $\mathbf{B} \times \mathbf{E}$
B) $\mathbf{E} \times \mathbf{B}$
C) $\mathbf{B}$
D) $\mathbf{E}$
E) $\mathbf{E}+\mathbf{B}$

Question 10

What is the wave number for a wavelength of $600 \mathrm{~nm}$ ?

A) $9.55 \times 10^{-8} \mathrm{~m}$
B) $600 \mathrm{~nm}$
C) $9.55 \times 10^{-8} \mathrm{~m}^{-1}$
D) $1.05 \times 10^{7} \mathrm{~m}^{-1}$
E) $1.67 \times 10^{6} \mathrm{~m}^{-1}$

Question 11

In vacuum, the components of an $\mathrm{EM}^{2}$ wave are $\mathrm{E}_{\mathrm{y}}=(50 \mathrm{~V} / \mathrm{m}) \cos \left[\left(5.00 \mathrm{~m}^{-1}\right) \mathrm{x}+\omega \mathrm{t}\right], \mathrm{E}_{\mathrm{x}}=0$ , and $\mathrm{E}_{\mathrm{z}}=0$ . In what direction is this wave moving?

A) positive $y$ -direction
B) negative $x$ -direction
C) positive $x$ -direction
D) positive or negative z-direction
E) negative y-direction

Question 12

In vacuum, the components of an $\mathrm{EM}$ wave are $\mathrm{E}_{\mathrm{y}}=(50 \mathrm{~V} / \mathrm{m}) \cos \left[\left(5.00 \mathrm{~m}^{-1}\right) \mathrm{x}+\omega \mathrm{t}\right], \mathrm{E}_{\mathrm{x}}=0$ , and $\mathrm{E}_{\mathrm{Z}}=0$ . What is the wavelength of the wave?

A) $1.26 \mathrm{~m}$
B) $2.52 \mathrm{~m}$
C) $5.00 \mathrm{~m}$
D) $0.200 \mathrm{~m}$
E) $0.796 \mathrm{~m}$

Question 13

In vacuum, the components of an $\mathrm{EM}$ wave are $\mathrm{E}_{\mathrm{y}}=(50 \mathrm{~V} / \mathrm{m}) \cos \left[\left(5.00 \mathrm{~m}^{-1}\right) \mathrm{x}+\omega \mathrm{t}\right], \mathrm{E}_{\mathrm{x}}=0$ , and $\mathrm{E}_{\mathrm{z}}=0$ . What is $\omega$ ?

A) $1.00 \times 10^{9} \mathrm{rad} / \mathrm{s}$
B) $1.50 \times 10^{9} \mathrm{rad} / \mathrm{s}$
C) $8.00 \times 10^{8} \mathrm{rad} / \mathrm{s}$
D) $1.20 \times 10^{9} \mathrm{rad} / \mathrm{s}$
E) More information is needed.

Question 14

In vacuum, the components of an $\mathrm{EM}$ wave are $\mathrm{E}_{\mathrm{y}}=(50 \mathrm{~V} / \mathrm{m}) \cos \left[\left(5.0 \mathrm{~m}^{-1}\right) \mathrm{x}+\omega \mathrm{t}\right], \mathrm{E}_{\mathrm{x}}=0$ , and $\mathrm{E}_{\mathrm{Z}}=0$ . What is the amplitude of the magnetic field for this wave?

A) $1.50 \times 10^{-6} \mathrm{~T}$
B) $1.67 \times 10^{-7} \mathrm{~T}$
C) $2.00 \times 10^{-7} \mathrm{~T}$
D) $5.00 \times 10^{-7} \mathrm{~T}$
E) $1.33 \times 10^{-6} \mathrm{~T}$

Question 15

If the intensity of radiation from the Sun is $1.4 \mathrm{~kW} / \mathrm{m}^{2}$ at a distance of $150 \times 10^{6} \mathrm{~km}$ , at what distance is the intensity $5.6 \mathrm{~kW} / \mathrm{m}^{2}$ ?

A) $75 \times 10^{6} \mathrm{~km}$
B) $38 \times 106 \mathrm{~km}$
C) $100 \times 10^{6} \mathrm{~km}$
D) $300 \times 10^{6} \mathrm{~km}$
E) less than $30 \times 10^{6} \mathrm{~km}$

Question 16

If a $20 \mathrm{~W}$ laser beam, which has an initial diameter of $2.0 \mathrm{~mm}$ , spreads out to a diameter of $2.0 \mathrm{~m}$ after traveling $10,000 \mathrm{~m}$ , what is the final intensity of the beam?

A) $20 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{2}$
B) $6.4 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{2}$
C) $20 \times 10^{-4} \mathrm{~W} / \mathrm{m}^{2}$
D) $20 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2}$
E) $6.4 \mathrm{~W} / \mathrm{m}^{2}$

Question 17

A $20 \mathrm{~W}$ laser beam, with an initial diameter of $2.0 \mathrm{~mm}$ , spreads out to a diameter of $2.0 \mathrm{~m}$ after traveling $10,000 \mathrm{~m}$ . What is the initial intensity of the beam?

A) $6.4 \times 10^{6} \mathrm{~W} / \mathrm{m}^{2}$
B) $1.0 \times 105 \mathrm{~W} / \mathrm{m}^{2}$
C) $2.0 \times 10^{5} \mathrm{~W} / \mathrm{m}^{2}$
D) $3.2 \times 10^{6} \mathrm{~W} / \mathrm{m}^{2}$
E) $20 \times 106 \mathrm{~W} / \mathrm{m}^{2}$

Question 18

A $20 \mathrm{~W}$ laser beam, with an initial diameter of $2.0 \mathrm{~mm}$ , spreads out to a diameter of $2.0 \mathrm{~m}$ after traveling $10,000 \mathrm{~m}$ . What is the initial $\mathrm{E}_{\mathrm{rms}}$ of the beam?

A) $1.9 \times 10^{2} \mathrm{~V} / \mathrm{m}$
B) $1.2 \times 10^{3} \mathrm{~V} / \mathrm{m}$
C) $4.9 \times 10^{4} \mathrm{~V} / \mathrm{m}$
D) $2.5 \times 10^{3} \mathrm{~V} / \mathrm{m}$
E) $1.7 \times 10^{2} \mathrm{~V} / \mathrm{m}$

Question 19

What is the intensity of the electromagnetic radiation $2.00 \mathrm{~m}$ from a $100 \mathrm{~W}$ isotropic source?

A) $1.99 \mathrm{~W} / \mathrm{m}^{2}$
B) $6.25 \mathrm{~W} / \mathrm{m}^{2}$
C) $25.0 \mathrm{~W} / \mathrm{m}^{2}$
D) $4.00 \mathrm{~W} / \mathrm{m}^{2}$
E) $1.00 \mathrm{~W} / \mathrm{m}^{2}$

Question 20

For electromagnetic radiation of intensity of $1.00 \mathrm{~W} / \mathrm{m}^{2}$ , what is the rms value of the electric field?

A) $6.45 \times 10^{-8} \mathrm{~V} / \mathrm{m}$
B) $9.11 \times 10^{-8} \mathrm{~V} / \mathrm{m}$
C) $9.69 \mathrm{~V} / \mathrm{m}$
D) $3.00 \times 10^{7} \mathrm{~V} / \mathrm{m}$
E) $19.4 \mathrm{~V} / \mathrm{m}$

Question 21

At the summer solstice in June, at what latitude is the Sun directly overhead at solar noon?

A) $23.5^{\circ} \mathrm{S}$
B) $23.5^{\circ} \mathrm{N}$
C) $40.0^{\circ} \mathrm{N}$
D) $66.5^{\circ} \mathrm{N}$
E) $0.0^{\circ}$ (the equator)

Question 22

Plane-polarized light of intensity $I_{0}$ is passed through a polarizer oriented at $45^{\circ}$ to the original plane of polarization. What is the intensity transmitted?

A) $0.35 \mathrm{I}_{0}$
B) 0.00
C) $0.70 \mathrm{I}_{0}$
D) $0.50 \mathrm{I}_{0}$
E) $0.25 \mathrm{I}_{0}$

Question 23

If unpolarized light with $\mathrm{E}_{\mathrm{rms}}=20 \mathrm{~V} / \mathrm{m}$ is passed through a polarizer, what is the transmitted $\mathrm{E}_{\mathrm{rms}}$ ?

A) $20 \mathrm{~V} / \mathrm{m}$
B) $5.0 \mathrm{~V} / \mathrm{m}$
C) $10 \mathrm{~V} / \mathrm{m}$
D) $7.1 \mathrm{~V} / \mathrm{m}$
E) $14 \mathrm{~V} / \mathrm{m}$

Question 24

Using the approximate formula for the Doppler shift, $\mathrm{f}_{\mathrm{o}} \approx \mathrm{f}_{\mathrm{S}}\left(1+\mathrm{v}_{\mathrm{rel}} / \mathrm{c}\right)$ one finds that a source is moving away at $0.60 \mathrm{c}$ . What result would the exact formula yield for the recession speed?

A) $0.40 \mathrm{c}$
B) $0.84 \mathrm{c}$
C) $0.54 \mathrm{c}$
D) $0.72 \mathrm{c}$
E) $0.60 \mathrm{c}$

Question 25

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

A) $5 \times 10^{7} \mathrm{~m} / \mathrm{s}$
B) $5 \times 105 \mathrm{~m} / \mathrm{s}$
C) $5 \times 106 \mathrm{~m} / \mathrm{s}$
D) $5 \times 104 \mathrm{~m} / \mathrm{s}$

Question 26

It is possible to detect Doppler shifts in the light emitted from each side of a rapidly spinning star. Suppose the light from a nearby star of radius $2.5 \times 10^{8} \mathrm{~km}$ is blue-shifted on one side of the star and red-shifted on the other side. Assume the center of mass of the star is stationary relative to Earth. If the star emits light of wavelength $525 \mathrm{~nm}$ that is shifted, in the received light, to $523 \mathrm{~nm}$ on one side of the star and to $527 \mathrm{~nm}$ on the other side, what is the rotational period of the star?

A) 34 days
B) 24 days
C) 32 days
D) 16 days

Question 27

It is possible to detect Doppler shifts in the light emitted from each side of a rapidly spinning star. Suppose the light from a nearby star of radius $2.5 \times 10^{8} \mathrm{~km}$ is blue-shifted on one side of the star and red-shifted on the other side. Assume the center of mass of the star is stationary relative to Earth. If the rotational period of the star is $72 \mathrm{~h}$ and the star emits (unshifted) light of wavelength $525 \mathrm{~nm}$ , what is the wavelength of the light received on Earth from the side of the star rotating toward us?

A) $504 \mathrm{~nm}$
B) $520 \mathrm{~nm}$
C) $546 \mathrm{~nm}$
D) $530 \mathrm{~nm}$
E) $514 \mathrm{~nm}$
F) $536 \mathrm{~nm}$

Question 28

Nexrad radar uses electromagnetic radiation of frequency of $2.7 \mathrm{GHz}$ to measure the speed of cloud systems. Radio waves from a transmitter are sent outward toward a cloud system, and the waves are reflected back toward the source. If the cloud system is moving, the reflected waves will be Doppler shifted. Suppose a Nexrad system observes clouds moving toward the transmitter at $21 \mathrm{~m} / \mathrm{s}$ . What is the difference between the transmitted and received frequencies of the radar in this case?

A) $570 \mathrm{~Hz}$
B) $190 \mathrm{~Hz}$
C) $380 \mathrm{~Hz}$
D) $760 \mathrm{~Hz}$

Question 29

At the Earth's surface, the intensity of solar radiation is approximately $1000 \mathrm{~W} / \mathrm{m}^{2}$ . If $1390 \mathrm{~W}$ are incident upon a $1.0 \mathrm{~m} \times 1.5 \mathrm{~m}$ window in a vertical, south-facing wall, what is the angle with respect to the vertical of the Sun's rays?

A) $68^{\circ}$
B) $22^{\circ}$
C) $44^{\circ}$
D) $61^{\circ}$
E) $29^{\circ}$
F) $46^{\circ}$