Deck 31: Properties of Light

Question 1

Light that has been traveling in a medium with an index of refraction n₂ is incident on the boundary surface of another medium with an index of refraction n₁.Given a sufficient angle of incidence,which of the following conditions must be satisfied for total internal reflection to occur?

A)n₁ < n₂
B)n₁ > n₂
C)n₁ = n₂
D)Any of these may be correct.
E)None of these is correct.

Answer 1

n₁ < n₂

Question 2

Ultra fast pulse lasers can emit pulses of the order 10 fs.If each pulse that is 10 fs long and the wavelength of the laser is 500 nm,the number of wavelengths in each pulse is

A)6
B)10
C)12
D)50
E)120

Answer 2

6

Question 3

From directly above,you're watching a fish swim 1.83 m beneath the surface of a clear lake (n = 1.33).How far beneath the surface does the fish seem to be?

A)0.914 m
B)1.37 m
C)1.83 m
D)2.44 m
E)2.93 m

Answer 3

1.37 m

Question 4

A ray of light passes from air into water,striking the surface of the water with an angle of incidence of 45º.Which of the following four quantities change as the light enters the water: (1)wavelength,(2)frequency,(3)speed of propagation,and (4)direction of propagation?

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

Question 5

A glass block with index of refraction 1.50 is immersed in water whose index of refraction is 1.33.The critical angle at the glass-water interface is

A)6.5º
B)41.9º
C)48.8º
D)56.3º
E)62.5º

Question 6

The speed of ultraviolet radiation in free space compared with the speed of visible radiation in free space is

A)very much greater.
B)a little greater.
C)the same.
D)a little less.
E)very much less.

Question 7

A light wave traveling at speed v₁ in medium 1 passes into medium 2 where its speed is v₂.By which of the following equations is the frequency f₁ of the wave in medium 1 related to its frequency f₂ in medium 2? ( $\theta$ ₁ and $\theta$ ₂ are the angles of incidence and refraction.)

A)f₁ sin $\theta$ ₁ = f₂ sin $\theta$ ₂
B)f₁v₂ = f₂v₁
C)f₁ = f₂
D)f₁v₁ = f₂v₂
E)f₁ sin $\theta$ ₂ = f₂ sin $\theta$ ₁

Question 8

Ultra fast pulse lasers can emit pulses of the order 10 fs.The length of each pulse that is 10 fs long is

A)1.0 $\mu$ m
B)2.0 $\mu$ m
C)3.0 $\mu$ m
D)9.0 $\mu$ m
E)12.0 $\mu$ m

Question 9

The speed of yellow sodium light in a certain liquid is 1.92 $\times$ 10⁸ m/s.With respect to air,the index of refraction of this liquid for sodium light is approximately

A)1.92
B)1.56
C)1.23
D)0.64
E)1.33

Question 10

Light is incident on a piece of glass in air at an angle of 37.0º from the normal.If the index of refraction of the glass is 1.50,the angle that the refracted ray makes with the normal is approximately

A)8.6º
B)21.8º
C)23.6º
D)41.8º
E)56.4º

Question 11

Which of the following statements is true about the speeds of the various colors of light in glass?

A)All colors of light have the same speed in glass.
B)violet has the highest speed,red the lowest
C)red has the highest speed,violet the lowest
D)green has the highest speed,red and violet the lowest
E)red and violet have the highest speed,green the lowest

Question 12

You are trying to catch fish by using a spear.You observe a large fish a couple of meters in front of you and a meter below the water surface.In order to hit the fish with your spear you must aim (assume that the fish is stationary and does not swim away in fright)

A)directly at the point where you see the fish.
B)slightly above the point where you see the fish.
C)slightly below the point where you see the fish.
D)slightly to the left side of the point where you see the fish.
E)slightly to the right side of the point where you see the fish.

Question 13

Light traveling in a transparent medium with an index of refraction n₁ is incident on a transparent boundary with a second transparent medium with an index n₂.Very little light is transmitted into the second medium.Which of the following statements must be true?

A)n₁ equals n₂
B)n₁ is somewhat greater than n₂
C)n₂ is somewhat greater than n₁
D)n₂ is much greater than n₁
E)Either index of refraction is much greater than the other

Question 14

Use the following figure for the next problem.
An object leaves point A and travels in a straight line to point B via path b.In region I,the speed is 100 m/s while in region II,the speed is 71 m/s.How long does it take for the object to go from A to B?

A)82.0 ms
B)70.8 ms
C)61.3 ms
D)34.3 ms
E)27.7 ms

Question 15

Communications satellites are usually placed in geosynchronous orbits,a distance of 4.43 $\times$ 10⁷ m from the center of Earth.What is the time lag for a signal sent from one point on Earth's surface to another via such a satellite? (The radius of Earth R_E = 6.370 $\times$ 10⁶ m.)

A)0.13 s
B)0.25 s
C)0.51 s
D)0.29 s
E)0.15 s

Question 16

Use the following figure for the next problem.
An object leaves point A and travels to point B via path a.In region I,the speed is 100 m/s while in region II,the speed is 71 m/s.How long does it take for the object to go from A to B?

A)80.0 ms
B)60.8 ms
C)40.6 ms
D)32.4 ms
E)26.8 ms

Question 17

Mission Control sends a brief wake-up call to astronauts in a distant spaceship.Five seconds after the call is sent,Mission Control hears the waking groans of the astronauts.How far away (at most)from Earth is the spaceship?

A)7.5 $\times$ 10⁸ m
B)15 $\times$ 10⁸ m
C)30 $\times$ 10⁸ m
D)45 $\times$ 10⁸ m
E)The spaceship is on the moon.

Question 18

As light passes from one medium into another,the angle of refraction is _____ in the medium with the _____ index of refraction and _____ speed of light.

A)smaller; larger; lower
B)smaller; larger; higher
C)larger; smaller; lower
D)larger; larger; lower
E)smaller; smaller; higher

Question 19

You see a fish in water at an apparent depth of 1.83 m.The actual depth of the fish,if the index of refraction of the water relative to air is 4/3,must be

A)3.81 cm
B)61.0 cm
C)1.37 m
D)1.83 m
E)2.44 m

Question 20

It has been suggested that a fundamental physical unit of time is the time required for light to traverse the diameter of the nucleus of an atom (approximately 3 $\times$ 10^-13 m).This unit of time is approximately

A)1 s
B)10^-4 s
C)2 $\times$ 10^-20 s
D)10^-21 s
E)10^-23 s

Question 21

The wavelength of green light in air is 500 nm.The wavelength of this light in glass of index of refraction 1.60 is approximately

A)313 nm
B)500 nm
C)750 nm
D)800 nm
E)427 nm

Question 22

Use the following figure below for the next problem.
The figure shows a cross-

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38.The numerical aperture of a fiber optic is defined as NA = n_air sin $\theta$ _m,where $\theta$ _m is the maximum incident angle so that the light ray is totally internally reflected inside the fiber.The NA for the fiber is

A)0.445
B)0.614
C)0.645
D)0.407
E)0.470

Question 23

A light wave traveling in air impinges on an amber plate at an angle of incidence of 60º.If the angle of refraction is 34º,the velocity of light in amber must be approximately

A)0.52 $\times$ 10⁸ m/s
B)4.64 $\times$ 10⁸ m/s
C)1.86 $\times$ 10³ m/s
D)2.09 $\times$ 10⁸ m/s
E)4.64 $\times$ 10¹⁰ m/s

Question 24

A small beam of monochromatic light in air is incident on a large plate of glass with plane-parallel sides at an angle of 30º.The index of refraction of the glass plate for this wavelength is 1.50.The angle of emergence of the light on the far side of the plate is approximately

A)30º
B)45º
C)20º
D)the angle whose sine is 1/3.
E)60º

Question 25

The dependence of the index of refraction on wavelength is called dispersion.A beam of light (in air)containing red and blue light is incident at an angle of 35 ^$\circ$ on a glass plate that has an index of refraction of 1.64 for blue light and 1.61 for red light.Calculate the angle between the red and blue light inside the glass.

A)1.3 ^$\circ$
B)0.40 ^$\circ$
C)0.56 ^$\circ$
D)0.74 ^$\circ$
E)0.13 ^$\circ$

Question 26

The dependence of the index of refraction on wavelength is called dispersion.A beam of light (in air)containing red and blue light is incident at an angle of 35 ^$\circ$ on a glass plate that has an index of refraction of 1.64 for blue light and 1.61 for red light.By what percent does the speed of the red light exceed that of the blue light inside the glass,i.e.calculate (v(red)-v(blue))* 100 / v(red)?

A)1.1%
B)1.8%
C)0.53%
D)The speed is the same for both colors.
E)0.019%

Question 27

Two clear but non-mixing liquids each of depth 15 cm are placed together in a glass container.The liquids have refractive indices of 1.75 and 1.33.What is the apparent depth of the combination when viewed from above?

A)19.8 cm
B)23.1 cm
C)17.7 cm
D)9.9 cm
E)None of these is correct.

Question 28

An "X" is marked on the bottom of a glass container.A microscope is adjusted so that it is focused on the "X." A liquid is now poured into the glass to a depth of 6.00 cm.If the microscope has to be backed up by a distance of 1.50 cm to refocus on the "X," then calculate the refractive index of the liquid.

A)1.25
B)4.00
C)1.33
D)0.75
E)3.00

Question 29

A 60 ^$\circ$ prism has a refractive index of 1.64 for blue light and 1.61 for red light.Calculate the difference in the angle of emergence from the opposite face of the prism for a beam of red and a beam of blue light that are both incident at an angle of 60^o.

A)0.4 ^$\circ$
B)0.0 ^$\circ$
C)1.3 ^$\circ$
D)3.9 ^$\circ$
E)2.7 ^$\circ$

Question 30

Use the following figure below for the next problem.
The figure shows a cross-

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38.What is the critical angle, $\theta$ _c,at the core-cladding interface?

A)44º
B)46º
C)55º
D)72º
E)None of these is correct.

Question 31

A 60 ^$\circ$ prism has a refractive index of 1.52.Calculate the angle of incidence for the initial light ray that is then refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.

A)41.1 ^$\circ$
B)18.9 ^$\circ$
C)29.4 ^$\circ$
D)30.6 ^$\circ$
E)60.6 ^$\circ$

Question 32

A light wave in air strikes a glass plate 1 cm thick at an angle of incidence of 50.0º.If the index of refraction of the glass is 1.50 for this light,the actual path length of the light through the glass is approximately

A)0.51 cm
B)1.16 cm
C)1.50 cm
D)2.11 cm
E)7.66 cm

Question 33

If the refractive index of glass is 1.5 and the refractive index of a particular liquid is 1.38,then calculate the value for the critical angle of total internal reflection at the liquid-glass interface.

A)23.1 ^$\circ$
B)66.9 ^$\circ$
C)82.8 ^$\circ$
D)42.6 ^$\circ$
E)None of these is correct.

Question 34

You shine light of frequency 4.00 $\times$ 10¹⁴ Hz through a glass plate whose index of refraction for this light is 1.50.The wavelength of this light in the glass is approximately

A)500 nm
B)110 nm
C)800 nm
D)425 nm
E)380 nm

Question 35

The minimum angle of deviation produced by a glass prism (n = 1.70 for the light used)whose apex angle is 45º is approximately

A)32º
B)36º
C)26º
D)18º
E)45º

Question 36

A column of liquid is 10 cm high.Viewed from above the liquid has an apparent depth of 6.77 cm.If the refractive index of the liquid is 1.33 at the top and increases uniformly to the bottom,then what is the refractive index at the bottom of the liquid?

A)1.96
B)2.95
C)1.48
D)1.62
E)None of these is correct.

Question 37

Use the following figure below for the next problem.
The figure shows a cross-

-A fiber optic is made by cladding a thin fiber core of refractive index n₁ = 1.45 with a material of refractive index n₂ = 1.38.What is the maximum incident angle, $\theta$ ,so that the light ray is totally internally reflected inside the fiber?

A)24.1º
B)26.4º
C)28.2º
D)30.3º
E)32.7º

Question 38

A 60 ^$\circ$ prism has a refractive index of 1.71.Calculate the angle of emergence out of the prism for a ray that enters one side at an angle almost parallel to one face,i.e.at 90 ^$\circ$ to the normal.

A)24.3 ^$\circ$
B)35.8 ^$\circ$
C)45.1 ^$\circ$
D)48.7 ^$\circ$
E)55.3 ^$\circ$

Question 39

The critical angle for light rays passing from flint glass (n = 1.70)into air is about

A)3.4º
B)36º
C)44º
D)54º
E)90º

Question 40

A 60 ^$\circ$ prism has a refractive index of 1.64 for blue light and 1.61 for red light.Calculate the difference in the angle of incidence for the initial red and blue light ray that is refracted inside the prism and just undergoes total internal reflection at the opposite face of the prism.

A)4.1 ^$\circ$
B)1.5 ^$\circ$
C)3.2 ^$\circ$
D)2.4 ^$\circ$
E)0.4 ^$\circ$

Question 41

Plane-polarized light cannot be produced by

A)dispersion
B)dichroism
C)reflection
D)scattering
E)refraction

Question 42

The index of refraction of plate glass is 1.50.The polarizing angle for light incident from air is

A)8.6º
B)33.7º
C)56.3º
D)81.5º
E)90º

Question 43

Light is circularly polarized if

A)the cross section of a spherical wave front is polarized.
B)it consists of two plane-polarized waves that are out of phase with each other by 90º.
C)it is refracted by a medium that has a high index of refraction.
D)it is reflected at the critical angle and polarized.
E)it is polarized by scattering from molecules.

Question 44

Two ideal polarizing sheets with their planes of polarization parallel to each other pass light of intensity I.If the planes are rotated in such a way that their planes of polarization make an angle of 40.0º,the intensity is approximately

A)0.293I
B)0.383I
C)0.502I
D)0.585I
E)0.770I

Question 45

When taking a picture of a highly reflecting surface,it is desirable to use a polarizer in front of the camera to cut down on the "glare".Suppose you are taking a picture of a lake where the water is very still.The polarizing axis of the polarizer should ideally be oriented

A)horizontally.
B)vertically.
C)at 30 ^$\circ$ .
D)at 45 ^$\circ$ .
E)in any direction.

Question 46

Of the following quantities,the one that is independent of the frequency of light is the

A)polarizing angle.
B)critical angle.
C)angle of minimum deviation.
D)angle of refraction.
E)angle of reflection.

Question 47

In any wave motion,dependence of velocity on wavelength is called

A)polarization
B)deviation
C)dispersion
D)diffraction
E)scattering

Question 48

Which of the following is not a phenomenon by which polarized light can be produced from unpolarized light?

A)absorption
B)reflection
C)birefringence
D)diffraction
E)scattering

Question 49

The index of refraction of a sample of glass cannot be determined by measuring the

A)Brewster's angle.
B)critical angle.
C)angle of minimum deviation.
D)ratio of true to apparent depth.
E)angle of dispersion between red and violet light.

Question 50

The optical phenomenon that is usually cited as demonstrating the transverse wave nature of light is

A)dispersion
B)interference
C)reflection
D)polarization
E)refraction

Question 51

Light known to be polarized in the horizontal direction is incident on a polarizing sheet.It is observed that only 15 percent of the intensity of the incident light is transmitted through the sheet.What angle does the transmission axis of the sheet make with the horizontal?

A)8.6º
B)21º
C)23º
D)67º
E)81º

Question 52

Light is incident at an angle of 60 ^$\circ$ at an air to glass interface.If the angle of refraction inside the glass is 32 ^$\circ$ ,then calculate the speed of light within the glass.

A)3.00 $\times$ 10⁸ m/s
B)1.77 $\times$ 10⁸ m/s
C)4.90 $\times$ 10⁸ m/s
D)1.84 $\times$ 10⁸ m/s
E)1.62 $\times$ 10⁸ m/s

Question 53

Two polarizers have their transmission axes at an angle $\theta$ .Unpolarized light of intensity I is incident on the first polarizer.What is the intensity of the light transmitted by the second polarizer?

A)I cos² $\theta$
B)0.5I cos² $\theta$
C)0.25I cos² $\theta$
D)I cos $\theta$
E)0.25I cos $\theta$

Question 54

Light is reflected from the surface of a lake (n = 1.33).What is the angle of incidence for which the reflected light is 100 percent polarized?

A)53º
B)49º
C)45º
D)41º
E)37º

Question 55

If you look at a dot on a piece of paper through a calcite crystal lying on the paper,you will see two images of the dot,one of which appears to be nearer to you than the other.From this evidence you can conclude that

A)the beams from both images are polarized.
B)calcite has different indices of refraction for the two beams.
C)there is interference between the two beams.
D)the calcite has increased the resolving power of your eye.
E)the appearance is due to diffraction.

Question 56

One would not attempt to polarize light by

A)selective absorption.
B)reflection from a surface.
C)passage through a narrow slit.
D)scattering.
E)double refraction.

Question 57

The index of refraction of water is approximately 1.33.The angle of incidence for maximum polarization by reflection from water is approximately

A)57º
B)53º
C)45º
D)37º
E)33º

Question 58

The fact that light can be polarized shows that it must be

A)a wave motion.
B)a transverse wave.
C)a longitudinal wave.
D)transmitted by waves of very short length.
E)monochromatic.

Question 59

An unpolarized beam of light is incident on a group of three polarizing sheets that are lined up so that the characteristic direction of each is rotated by 45º clockwise with respect to the preceding sheet.The fraction of the incident intensity I_o that is transmitted is

A)zero
B)I_o/2
C)I_o/4
D)I_o/6
E)I_o/8

Question 60

Light is an electromagnetic wave.When visible light is plane polarized,

A)the electric-field vector is parallel to the magnetic-field vector.
B)the electric-field vector is parallel to the direction of propagation.
C)the electric-field vector is in a fixed direction perpendicular to the direction of propagation,but the magnetic-field vector may be in any direction.
D)the electric-field vector is in a fixed direction perpendicular to the direction of propagation,and the magnetic-field vector is perpendicular to the electric-field vector.
E)None of these is correct.

Question 61

The energy of an electromagnetic wave that is in the red region of the visible spectrum is approximately

A)1 eV
B)2 eV
C)3 eV
D)4 eV
E)5 eV

Question 62

If the wavelength $\lambda$ of the incident light is large compared with the size of the atom,the probability of elastic scattering varies as

A) $\lambda$
B) $\lambda$ ⁴
C) $\lambda$ ^-4
D) $\lambda$ ²
E) $\lambda$ ^-3

Question 63

The photon energy for light of wavelength 500 nm is approximately

A)1.77 eV
B)3.10 eV
C)6.20 eV
D)2.48 eV
E)5.46 eV

Question 64

Use the following figure to answer the next problem.

-If the index of refraction of the glass plate shown is 1.45,the angle of incidence $\theta$ ₁ that will cause the unpolarized light to be reflected as completely plane-polarized light is

A)8.25º
B)34.6º
C)45.0º
D)55.4º
E)81.7º

Question 65

The index of refraction of water is 1.33.The angle of incidence for maximum polarization by reflection is approximately

A)57º
B)53º
C)45º
D)37º
E)33º

Question 66

A light wave is like a sound wave in that both

A)are longitudinal waves.
B)are means of transmitting energy.
C)are transverse waves.
D)require a material medium for propagation.
E)have the same velocity in air.

Question 67

"To find the value of the resultant displacement for overlapping waves at any point at a particular instant,it is only necessary to add the values of the displacements for the individual waves." This is a statement of

A)Huygens' principle.
B)the principle of superposition.
C)Bernoulli's principle.
D)the principle of dispersion.
E)Newton's theory of light.

Question 68

Use the following figure for the next problem.
The film shows the line spectrum of an unknown element.If the wavelengths of lines (a),(b)and (c)are 410 nm,500 nm and 556 nm respectively,then the color of line (d)is

A)violet
B)blue
C)green
D)yellow
E)red

Question 69

Sound waves differ from light waves in many respects.One important difference is that sound waves cannot

A)be refracted.
B)be reflected.
C)show interference.
D)show diffraction.
E)be polarized.

Question 70

Use the following figure for the next problem.
The film shows the line spectrum of an unknown element.If the wavelengths of lines (a),(b)and (c)are 410 nm,500 nm and 556 nm respectively,then the wavelength for line (d)is

A)590 nm
B)600 nm
C)615 nm
D)625 nm
E)635 nm

Question 71

The wavelength light that has of a photon energy of 4.25 eV is

A)292 nm
B)973 nm
C)706 nm
D)1559 nm
E)None of these is correct.

Question 72

The principle of superposition states:

A)The effect observed at each point of a wave made up of two or more waves is the sum of the effects that the individual waves would produce at that point.
B)Huygens' wavelets cannot be allowed to extend across regions where the phase velocity of the wave changes abruptly.
C)Sources of radiation whose phase angles are maintained at constant differences are said to be coherent.
D)A characteristic phenomenon of wave propagation is the tendency of a wave to expand around and behind any obstacles it chances to encounter.
E)A good source of waves at a particular frequency is a good detector of waves at the same frequency.

Question 73

The lifetime of a typical excited atomic energy state is of the order of

A)10^-6 s
B)10^-7 s
C)10^-8 s
D)10^-9 s
E)10^-10 s

Question 74

Huygens' theory for the construction of wavefronts states that

A)the angle of incidence is always less than the angle of refraction.
B)the time required for light to travel from one point to another is either a maximum or minimum.
C)only parallel light produces interference and diffraction.
D)each point on a wavefront is itself the source of a secondary spherical wave.
E)all wavefronts are spherical.

Question 75

Use the following figure to answer the next problem.
The plane of polarization of the reflected light lies

A)parallel to the page.
B)at 45º with respect to the page.
C)at 34.6º with respect to the page.
D)at 55.4º with respect to the page.
E)perpendicular to the page.

Question 76

Which of the following is not a property of all waves?

A)refraction
B)diffraction
C)reflection
D)interference
E)polarization

Question 77

The frequency of light that has a photon energy of 3.5 eV is

A)9.55 $\times$ 10¹⁴ Hz
B)9.55 $\times$ 10¹⁵ Hz
C)8.46 $\times$ 10¹⁵ Hz
D)6.53 $\times$ 10¹⁵ Hz
E)4.78 $\times$ 10¹⁵ Hz

Question 78

Four perfectly polarizing plates are stacked so that the axis of each plate is turned 30º clockwise with respect to that of the plate above it.The percentage of the incident unpolarized light that is transmitted by the stack is approximately

A)zero
B)0.78%
C)6.3%
D)21%
E)27%

Question 79

When light is reflected from a plane surface of glass at the polarizing angle,the

A)reflected ray is at right angles to the incident ray.
B)angle of reflection is equal to the angle of refraction.
C)incident ray is at right angles to the refracted ray.
D)reflected ray is at right angles to the refracted ray.
E)intensity of the reflected light is a maximum.

Question 80

If light reflected from a transparent substance at an angle of 58.0º is completely plane polarized,light incident at an angle of 32.0º is refracted at an angle of

A)32.0º
B)58.0º
C)19.3º
D)90.0º
E)70.7º