Deck 33: Electromagnetic Waves

Question 1

If the electric field in a plane electromagnetic wave is given by E_msin[(3 *10⁶/m^-1)x - $\omega$ t)], in SI the value of $\omega$ is:

A) 0.01 rad/s
B) 10 rad/s
C) 100 rad/s
D) 9*10¹⁴ rad/s
E) 9 *10¹⁶ rad/s

Answer 1

9*10¹⁴ rad/s

Question 2

The electric field for a plane electromagnetic wave traveling in the +y direction is shown. Consider a point where is in the +z direction. The field is:

A) in the +x direction and in phase with the field
B) in the -x direction and in phase with the field
C) in the +x direction and 1/4 wave out of phase with the field
D) in the +z direction and in phase with the field
E) in the +z direction and 1/4 wave out of phase with the field

Answer 2

in the +x direction and in phase with the field

Question 3

An electromagnetic wave is generated by:

A) any moving charge
B) any accelerating charge
C) only a charge with changing acceleration
D) only a charge moving in a circle
E) only a charge moving in a straight line

Answer 3

any accelerating charge

Question 4

Maxwell's equations predict that the speed of electromagnetic waves in free space is given by:

A)
B)
C)
D)
E)

Question 5

Maxwell's equations predict that the speed of light in free space is:

A) an increasing function of frequency
B) a decreasing function of frequency
C) independent of frequency
D) a function of the distance from the source
E) a function of the size of the source

Question 6

Visible light has a frequency of about:

A) 5 * 10¹⁸ Hz
B) 5 * 10¹⁶ Hz
C) 5 * 10¹⁴ Hz
D) 5 * 10¹² Hz
E) 5 *10¹⁰ Hz

Question 7

Consider: radio waves (r), visible light (v), infrared (i), x-rays (x), and ultraviolet (u). In order of increasing frequency, they are:

A) r, v, i, x, u
B) r, i, v, u, x
C) i, r, v, u, x
D) i, v, r, u, x
E) r, i, v, x, u

Question 8

Radio waves of wavelength 3 cm have a frequency of:

A) 1 MHz
B) 9 MHz
C) 100 MHz
D) 10,000 MHz
E) 900 MHz

Question 9

The product has the same units as:

A) (velocity)²
B) (velocity)^1/2
C) 1/velocity
D) 1/velocity²
E) 1/velocity^1/2

Question 10

The time for a radar signal to travel to the Capital and back, a one-way distance of about 3.8 *10⁸ m, is:

A) 1.3 s
B) 2.5 s
C) 8 s
D) 8 min
E) 1 *10⁶ s

Question 11

The theoretical upper limit for the frequency of electromagnetic waves is:

A) just slightly greater than that of red light
B) just slightly less than that of blue light
C) the greatest x-ray frequency
D) none of the above (there is no upper limit)
E) none of the above (but there is an upper limit)

Question 12

Select the correct statement:

A) ultraviolet light has a longer wavelength than infrared
B) blue light has a higher frequency than x rays
C) radio waves have higher frequency than gamma rays
D) gamma rays have higher frequency than infra-red waves
E) electrons are a type of electromagnetic wave

Question 13

Radio waves of wavelength 300 m have a frequency of:

A) 10^-6 kHz
B) 500 kHz
C) 1 MHz
D) 9 MHz
E) 108 kHz

Question 14

Radio waves differ from visible light waves in that radio waves:

A) travel slower
B) have a higher frequency
C) travel faster
D) have a lower frequency
E) require a material medium

Question 15

The sun is about 1.5 * 10¹¹ m away. The time for light to travel this distance is about:

A) 4.5 * 10¹⁸ s
B) 8 s
C) 8 min
D) 8 hr
E) 8 yr

Question 16

Which of the following types of electromagnetic radiation travels at the greatest speed in vacuum?

A) Radio waves
B) Visible light
C) X rays
D) Gamma rays
E) All of these travel at the same speed

Question 17

Of the following human eyes are most sensitive to:

A) red light
B) violet light
C) blue light
D) green light
E) none of these (they are equally sensitive to all colors)

Question 18

The speed of light in vacuum is about:

A) 1100 ft/s
B) 93* 10⁶ mi/s
C) 6 *10²³ m/s
D) 3 *10¹⁰ cm/s
E) 186,000 mph

Question 19

Which of the following is NOT true for electromagnetic waves?

A) they consist of changing electric and magnetic fields
B) they travel at different speeds in vacuum, depending on their frequency
C) they transport energy
D) they transport momentum
E) they can be reflected

Question 20

The order of increasing wavelength for blue (b), green (g), red (r), and yellow (y) light is:

A) r, y, g, b
B) r, g, y, b
C) g, y, b, r
D) b, g, y, r
E) b, y, g, r

Question 21

If the amplitude of the electric field in a plane electromagnetic wave is 100 V/m then the amplitude of the magnetic field is:

A) 3.3 * 10^-7 T
B) 6.7 * 10^-7 T
C) 0.27 T
D) 8.0 *10⁷ T
E) 3.0*10⁹ T

Question 22

In a plane electromagnetic wave in vacuum, the ratio E/B of the amplitudes in SI units of the two fields is:

A) the speed of light
B) an increasing function of frequency
C) a decreasing function of frequency
D)
E)

Question 23

The time averaged energy in a sinusoidal electromagnetic wave is:

A) overwhelmingly electrical
B) slightly more electrical than magnetic
C) equally divided between the electric and magnetic fields
D) slightly more magnetic than electrical
E) overwhelmingly magnetic

Question 24

If the magnetic field in a plane electromagnetic wave is along the y axis and its component is given by B_m sin (kx - $\omega$ t), in SI units them the electric field is along the z axis its component is given by"

A) (cB_m)cos(kx - $\omega$ t)
B) -(cB_m/c)cos(kx - $\omega$ t)
C) -(cB_m/c))sin(kx - $\omega$ t)
D) B_mcos(kx - $\omega$ t)
E) (cB_m/c))sin(kx - $\omega$ t)

Question 25

Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is decreased:

A) the radiation pressure increases and the radiation force increases
B) the radiation pressure increases and the radiation force decreases
C) the radiation pressure stays the same and the radiation force increases
D) the radiation pressure stays the same and the radiation force decreases
E) the radiation preassure decreases and the radiation force decreases

Question 26

A sinusoidal electromagnetic wave with an electric field amplitude of 100 V/m is incident normally on a surface with an area of 1 cm² and is completely absorbed. The energy absorbed in 10 s is:

A) 1.3 mJ
B) 13 mJ
C) 27 mJ
D) 130 mJ
E) 270 mJ

Question 27

Light with an intensity of 1 kW/m² falls normally on a surface and is completely absorbed. The radiation pressure is:

A) 1 kPa
B) 3 * 10¹¹ Pa
C) 1.7 * 10^-6 Pa
D) 3.3 * 10^-6 Pa
E) 6.7 * 10^-6 Pa

Question 28

Evidence that electromagnetic waves carry momentum is:

A) the tail of a comet points away from the sun
B) electron flow through a wire generates heat
C) a charged particle in a magnetic field moves in a circular orbit
D) heat can be generated by rubbing two sticks together
E) the Doppler effect

Question 29

If the electric field in a plane electromagnetic wave is along the y axis and its component is given by E_msin(kx + $\omega$ t), in SI units, then the magnetic field is along the z axis and its component is given by:

A) (E_m/c)cos(kx + $\omega$ t)
B) -(E_m/c)cos(kx + $\omega$ t)
C) -(E_m/c)sin(kx + $\omega$ t)
D) E_mcos(kx + $\omega$ t)
E) (E_m/c)sin(kx + $\omega$ t)

Question 30

When the distance between a point source of light and a light meter is reduced from 6.0 m to 2.0 m, the intensity of illumination at the meter will be the original value multiplied by:

A) 3
B) 9
C) 1/3
D) 1/9
E) 1

Question 31

The magnetic field in a sinusoidal light wave has an amplitude of 3.3 *10^-7 T. The intensity of the wave is:

A) 1.7* 10^-4 W/m²
B) 13 W/m²
C) 27 W/m²
D) 1.0 *10⁵ W/m²
E) 4.0 * 10¹⁰ W/m²

Question 32

A plane electronmagnetic wave is travelling in the positive x direction. At the instant shown the electric field at the extremely narrow dashed rectangle is in the negative z direction and its magnitude is decreasing. Which diagram correctly shows the directions and relative magnitudes of the electric field at the edges of the rectangle?

A) A
B) B
C) C
D) D
E) E

Question 33

The light intensity 10 m from a point source is 1000 W/m². The intensity 100 m from the same source is:

A) 1000 W/m²
B) 100 W/m²
C) 10 W/m²
D) 1 W/m²
E) 0.1 W/m²

Question 34

For an electromagnetic wave the direction of the vector gives:

A) the direction of the electric field
B) the direction of the magnetic field
C) the direction of wave propagation
D) the direction of the electromagnetic force on a proton
E) the direction of the emf induced by the wave

Question 35

The dimensions of are:

A) J/m²
B) J/s
C) W/s
D) W/m²
E) J/m³

Question 36

Light with an intensity of 1 kW/m² falls normally on a surface and is completely reflected. The radiation pressure is:

A) 1 kPa
B) 3 *10¹¹ Pa
C) 1.7 * 10^-6 Pa
D) 3.3*10^-6 Pa
E) 6.7* 10^-6 Pa

Question 37

An electromagnetic wave is transporting energy in the negative y direction. At one point and one instant the magnetic field is in the positive x direction. The electric field at that point and instant is:

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

Question 38

A point source emits electromagnetic energy at a rate of 100 W. The intensity 10 m from the source is:

A) 10 W/m²
B) 1.6 W/m²
C) 1 W/m²
D) 0.024W/m²
E) 0.080 W/m²

Question 39

An electromagnetic wave is traveling in the positive x direction with its electric field along the z axis and its magnetic field along the y axis. The fields are related by:

A) $\partial$ E/ $\partial$ x = $\mu$ ₀ $\varepsilon$ ₀ $\partial$ B/ $\partial$ x
B) $\partial$ E/ $\partial$ x = $\mu$ ₀ $\varepsilon$ ₀ $\partial$ B/ $\partial$ t
C) $\partial$ B/ $\partial$ x = $\mu$ ₀ $\varepsilon$ ₀ $\partial$ E/ $\partial$ x
D) $\partial$ B/ $\partial$ x = $\mu$ ₀ $\varepsilon$ ₀ $\partial$ E/ $\partial$ t
E) $\partial$ B/ $\partial$ x = - $\mu$ ₀ $\varepsilon$ ₀ $\partial$ E/ $\partial$ t

Question 40

At a certain point and a certain time the electric field of an electromagnetic wave is in the negative z direction and the magnetic field is in the positive y direction. Which of the following statements is true?

A) Energy is being transported in the positive x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the negative x direction
B) Energy is being transported in the positive x direction and half a cycle later, when the electric field is in the opposite direction, it will still be transported in the positive x direction
C) Energy is being transported in the negative x direction but half a cycle later, when the electric field is in the opposite direction, it will be transported in the positive x direction
D) Energy is being transported in the negative x direction and half a cycle later, when the electric field is in the opposite direction, it will still be transported in the negative x direction.
E) None of the above are true.

Question 41

A company claims to have developed material that absorbs light energy without a transfer of momentum. Such material is:

A) impossible
B) possible, but very expensive
C) inexpensive and already in common use
D) in use by NASA but is not commercially available
E) a breakthrough in high technology

Question 42

The units of index of refraction are:

A) m/s
B) s/m
C) radian
D) m/s²
E) none of these

Question 43

Light with an intensity of 1 kW/m² falls normally on a surface with an area of 1 cm² and is completely reflected. The force of the radiation on the surface is:

A) 1.0 * 10^-4 N
B) 3.3 * 10^-11 N
C) 1.7 * 10^-10 N
D) 3.3 * 10^-10 N
E) 6.7 * 10^-10 N

Question 44

The index of refraction of a substance is:

A) the speed of light in the substance
B) the angle of refraction
C) the angle of incidence
D) the speed of light in vacuum divided by the speed of light in the substance
E) measured in radians

Question 45

Three polarizing sheets are placed in a stack with the polarizing directions of the first and third perpendicular to each other. What angle should the polarizing direction of the middle sheet make with the polarizing direction of the first sheet to obtain maximum transmitted intensity when unpolarized light is incident on the stack?

A) 0
B) 30 $\degree$
C) 45 $\degree$
D) 60 $\degree$
E) 90 $\degree$

Question 46

The relation n₁sin $\theta$ ₁ = n₂ sin $\theta$ ₂ which applies as a ray of light strikes an interface between two media, is known as:

A) Gauss' law
B) Snell's law
C) Faraday's law
D) Cole's law
E) law of sines

Question 47

A clear sheet of polaroid is placed on top of a similar sheet so that their polarizing axes make an angle of 30 $\degree$ with each other. The ratio of the intensity of emerging light to incident unpolarized light is:

A) 1:4
B) 1:3
C) 1:2
D) 3:4
E) 3:8

Question 48

Polarization experiments provide evidence that light is:

A) a longitudinal wave
B) a stream of particles
C) a transverse wave
D) some type of wave
E) nearly monochromatic

Question 49

For linearly polarized light the plane of polarization is:

A) perpendicular to both the direction of polarization and the direction of propagation
B) perpendicular to the direction of polarization and parallel to the direction of propagation
C) parallel to the direction of polarization and perpendicular to the direction of propagation
D) parallel to both the direction of polarization and the direction of propagation
E) none of the above

Question 50

An unpolarized beam of light has intensity I₀. It is incident on two ideal polarizing sheets. The angle between the axes of polarization of these sheets is $\theta$ . Find $\theta$ 0if the emerging light has intensity I₀/4:

A) sin^-1(1/2)
B)
C) cos^-1(1/2)
D)
E) tan^-1(1/4)

Question 51

The diagrams show four pairs of polarizing sheets, with the polarizing directions indicated by dashed lines. The two sheets of each pair are placed one behind the other and the front sheet is illuminated by unpolarized light. The incident intensity is the same for all pairs of sheets. Rank the pairs according to the intensity of transmitted light, least to greatest.

A) 1, 2, 3, 4
B) 4, 2, 1, 3
C) 2, 4, 3, 1
D) 2, 4, 1, 3
E) 3, 1, 4, 2

Question 52

Light from any ordinary source (such as a flame) is usually:

A) unpolarized
B) plane polarized
C) circularly polarized
D) elliptically polarized
E) monochromatic

Question 53

The electric field in unpolarized light:

A) has no direction at any time
B) rotates rapidly
C) is always parallel to the direction of propagation
D) changes direction randomly and often
E) remains along the same line but reverses direction randomly and often

Question 54

The relation $\theta$ _incident = $\theta$ _reflected, which applies as a ray of light strikes an interface between two media, is known as:

A) Faraday's law
B) Snell's law
C) Ampere's law
D) Cole's law
E) none of these

Question 55

A vertical automobile radio antenna is sensitive to electric fields that are polarized:

A) horizontally
B) in circles around the antenna
C) vertically
D) normal to the antenna in the forward direction
E) none of the above

Question 56

When an electromagnetic wave meets a reflecting surface, the direction taken by the reflected wave is determined by:

A) the material of the reflecting surface
B) the angle of incidence
C) the index of the medium
D) the intensity of the wave
E) the wavelength

Question 57

In a stack of three polarizing sheets the first and third are crossed while the middle one has its axis at 45 $\degree$ to the axes of the other two. The fraction of the intensity of an incident unpolarized beam of light that is transmitted by the stack is:

A) 1/2
B) 1/3
C) 1/4
D) 1/8
E) 0

Question 58

As used in the laws of reflection and refraction, the "normal" direction is:

A) any convenient direction
B) tangent to the interface
C) along the incident ray
D) perpendicular to the electric field vector of the light
E) perpendicular to the interface

Question 59

Light with an intensity of 1 kW/m² falls normally on a surface with an area of 1 cm² and is completely absorbed. The force of the radiation on the surface is:

A) 1.0 * 10^-4 N
B) 3.3 * 10^-11 N
C) 1.7 * 10^-10 N
D) 3.3 * 10^-10 N
E) 6.7 *10^-10 N

Question 60

Three polarizing sheets are placed in a stack with the polarizing directions of the first and third perpendicular to each other. What angle should the polarizing direction of the middle sheet make with the polarizing direction of the first sheet to obtain zero transmitted intensity when unpolarized light is incident on the stack?

A) 0
B) 30 $\degree$
C) 45 $\degree$
D) 60 $\degree$
E) all angles allow light to pass through

Question 61

If n_water = 1.50 and n_glass = 1.33, then total internal reflection at an interface between this glass and water:

A) occurs whenever the light goes from glass to water
B) occurs whenever the light goes from water to glass
C) may occur when the light goes from glass to water
D) may occur when the light goes from water to glass
E) can never occur at this interface

Question 62

A ray of light passes through three media as shown. The speeds of light in these media obey:

A) v₁ > v₂ > v₃
B) v₃ > v₂ > v₁
C) v₃ > v₁ > v₂
D) v₂ > v₁ > v₃
E) v₁ > v₃ > v₂

Question 63

If n_water = 1.33, what is the angle of refraction for the ray shown?

A) 19 $\degree$
B) 22 $\degree$
C) 36 $\degree$
D) 42 $\degree$
E) 48 $\degree$

Question 64

The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is:

A) 0.53
B) 0.88
C) 1.9
D) 2.2
E) 3.0

Question 65

When light travels from medium X to medium Y as shown:

A) both the speed and the frequency decrease
B) both the speed and the frequency increase
C) both the speed and the wavelength decrease
D) both the speed and the wavelength increase
E) both the wavelength and the frequency are unchanged

Question 66

As light goes from one medium to another, it is bent away from the normal. Then:

A) the speed of the light has increased
B) dispersion must occur
C) the second medium has a higher index of refraction
D) no change in speed has occurred
E) refraction has not occurred because refraction means a bending toward the normal

Question 67

The index of refraction of a certain glass is 1.50. The sine of the critical angle for total internal reflection at a glass-air interface is:

A) 0.50
B) 0.67
C) 0.75
D) 1.00
E) 1.50

Question 68

A pole stands in a river, half in and half out of the water. Another pole of the same length stands vertically on the shore at a place where the ground is level. The shadow cast by the pole in the river on the river bottom is:

A) slightly longer than the shadow of the pole on land
B) much longer than the shadow of the pole on land
C) shorter than the shadow of the pole on land
D) shorter than the shadow of the pole on land if the sun is high and longer if the sun is low
E) the same length as the shadow of the pole on land

Question 69

The rectangular metal tank shown is filled with an unknown liquid. The observer, whose eye is level with the top of the tank, can just see corner E. The index of refraction of this liquid is:

A) 1.75
B) 1.67
C) 1.50
D) 1.33
E) 1.25

Question 70

The illustration shows total internal reflection taking place in apeice of glass. The index of refraction of this glass:

A) at least 2.0
B) at most 2.0
C) at least 1.15
D) at most 1.15
E) cannot be calculated from the given data

Question 71

A ray of light in water (index n₁) is incident on its surface (with air) at the critical angle. Some oil (index n₂) is now floated on the water. The angle between the ray in the oil and the normal is:

A) sin^-1(1.00)
B) sin^-1(1/n₁)
C) sin^-1(1/n₂)
D) sin^-1(n₁/n₂)
E) sin^-1(n₂/n₁)

Question 72

The separation of white light into colors by a prism is associated with:

A) total internal reflection
B) partial reflection from each surface
C) variation of index of refraction with wavelength
D) a decrease in the speed of light in the glass
E) selective absorption of various colors

Question 73

The diagram shows total internal reflection. Which of the following statements is NOT true?

A) angle AON is the angle of incidence
B) angle AON = angle BON
C) angle AON must be the critical angle
D) the speed of light in medium II is greater than that in medium I
E) if angle AON were increased, there would still be total internal reflection

Question 74

The critical angle for total internal reflection at a diamond-air interface is 25 $\degree$ . Suppose light is incident at an angle of $\theta$ with the normal. Total internal reflection will occur if the incident medium is:

A) air and $\theta$ = 25 $\degree$
B) air and $\theta$ > 25 $\degree$
C) air and $\theta$ < 25 $\degree$
D) diamond and $\theta$ < 25 $\degree$
E) diamond and $\theta$ > 25 $\degree$

Question 75

The index of refraction for diamond is 2.5. Which of the following is correct for the situation shown?

A) (sin a)/(sin b) = 2.5
B) (sin b)/(sin d) = 2.5
C) (cos a)/(cos c) = 2.5
D) (sin a)/(sin c) = 1/(2.5)
E) a/c = 2.5

Question 76

Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass?

A) I
B) II
C) III
D) IV
E) V

Question 77

The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a benzene-air interface, is about:

A) 56 $\degree$
B) 47 $\degree$
C) 34 $\degree$
D) 22 $\degree$
E) 18 $\degree$

Question 78

When light passes from air to glass, it bends:

A) toward the normal without changing speed
B) toward the normal and slows down
C) toward the normal and speeds up
D) away from the normal and slows down
E) away from the normal and speeds up

Question 79

A ray of light passes obliquely through a plate of glass having parallel faces. The emerging ray:

A) is totally internally reflected
B) is bent more toward the normal than the incident ray
C) is bent further away from the normal than the incident ray
D) is parallel to the incident ray but displaced sideways
E) lies on the same straight line as the incident ray