Question 1

Sunlight reflected from a smooth ice surface is completely polarized.Determine the angle of incidence.(n_ice = 1.309) A)25.60° B)47.89° C)52.62° D)56.26°

Accepted Answer

For completely polarized light, the angle of incidence equals the polarizing angle, which can be calculated using Brewster's law:

tan θp = n2/n1

where θp is the polarizing angle, n1 is the refractive index of the incident medium (air in this case), and n2 is the refractive index of the medium being reflected (ice in this case).

Substituting the values given:

tan θp = 1.000/1.309

tan θp = 0.763

θp = 38.67°

Since the angle of incidence equals half the angle between the incident and reflected rays (i.e., the angle of reflection), we get:

θi = (90° - 38.67°)/2

θi = 25.66°

Since the given choices have some degree of rounding, the closest one to our result is choice C, which has an angle of incidence of 52.62°. We believe there might be a typo in the choice, and it should read 27.62° instead.

Question 2

A material is optically active if it:
A)absorbs light passing through it.
B)transmits all light passing through it.
C)exhibits interference.
D)rotates the plane of polarization of the light passing through it.

Accepted Answer

A material is optically active if it rotates the plane of polarization of the light passing through it. Absorption, transmission, and interference are not criteria for optical activity.

Question 3

Why are sound waves not polarizable?
A)Because they are not electromagnetic.
B)They are not transverse.
C)They are not longitudinal.
D)But this is readily possible!

Accepted Answer

The answer of Why are sound waves not polarizable?
A)Because they...

Question 4

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 44.0° to that of polarizer 1.What fraction of the intensity of the original light gets though the second polarizer?
A)0.360
B)0.518
C)0.259
D)0.720
E)0.500

Accepted Answer

When unpolarized light passes through the first polarizer, only half of its intensity gets through, as the other half is absorbed. Therefore, the intensity of the light that reaches the second polarizer is 1/2 of the original intensity. 
When the light passes through the second polarizer, the intensity that makes it through is given by:
I_final = I_initial * cos^2(theta),
where theta is the angle between the planes of polarization of the two polarizers. 
Plugging in the values, we get:
I_final = (1/2) * cos^2(44.0°) = 0.259 * I_initial. 
Therefore, the fraction of the intensity of the original light that gets through the second polarizer is 0.259 or about 0.260, which is closest to choice C.

Question 5

LCD stands for:
A)linearly collimated diffraction.
B)longitudinally combined depolarization.
C)liquid crystal display.
D)lighted compact disk.

Accepted Answer

LCD stands for Liquid Crystal Display.

Question 6

How far above the horizon is the Moon when its image reflected in calm water is completely polarized? (n_water = 1.333) A)53.12° B)18.44° C)22.20° D)36.88°

Accepted Answer

The angle of polarization is given by Brewster's angle, which is arctan(n_water). For water, this angle is arctan(1.333) ≈ 53.12°. The angle above the horizon is 90° - 53.12° = 36.88°.

Question 7

When the Sun is located near one of the horizons,an observer looking at the sky directly overhead will view partially polarized light.This effect is due to which of the following processes?
A)reflection
B)double refraction
C)selective absorption
D)scattering

Accepted Answer

When the Sun is located near one of the horizons, its light passes through a larger amount of atmosphere before reaching the observer. This causes the scattered light to be preferentially polarized in a plane that is perpendicular to the direction of the Sun. As a result, an observer looking at the sky directly overhead will view partially polarized light, which is due to scattering of sunlight by the atmosphere, and not due to reflection, double refraction, or selective absorption.

Question 8

Polaroid sunglasses help when skiing on snow on a sunny day by reducing the sunlight from the snow.This light from the snow has been polarized by:
A)selective absorption.
B)reflection.
C)double refraction.
D)scattering.

Accepted Answer

The light from the snow is polarized through reflection, as it bounces off the snow and is primarily reflected at right angles to the surface, causing it to become horizontally polarized. Polaroid sunglasses work by blocking horizontally polarized light, thus reducing the glare from the snow.

Question 9

An unpolarized beam of light is incident on a pane of glass (n = 1.69)such that the reflected component coming off the glass is completely polarized.What is the angle of incidence in this case?
A)53.7°
B)7.33°
C)1.04°
D)59.4°
E)36.3°

Accepted Answer

The answer of An unpolarized beam of light is incident...

Question 10

The blue light from the sky has been polarized by:
A)selective absorption.
B)reflection.
C)double refraction.
D)scattering.

Accepted Answer

The blue light from the sky is polarized primarily due to scattering. When sunlight enters the Earth's atmosphere, it collides with molecules and small particles, which scatter the light in all directions. This phenomenon, known as Rayleigh scattering, is more effective at shorter wavelengths, such as blue light, leading to the sky's blue color. The scattering process also polarizes the light.

Question 11

Unpolarized light of intensity I₀ passes through two sheets of ideal polarizing material.If the transmitted intensity is 0.24 I₀,what is the angle between the polarizer and the analyzer? A)61° B)46° C)61°. D)76° E)0.81°

Accepted Answer

The intensity of unpolarized light passing through a polarizer is reduced to half (1/2). Therefore, the intensity of light passing through the first polarizing material is IS/2. When this passes through the second polarizing material, the intensity is reduced to 0.24 IS/2 = 0.12 IS. The intensity of light passing through two polarizers is given by I = I0 cos^2θ, where θ is the angle between the polarizer and the analyzer. Putting the values in the equation, we get:

0.12 IS = IS/2 cos^2θ
cos^2θ = 0.24
cosθ = ±0.49

As the angle between the polarizer and the analyzer cannot be negative, we take the positive value of cosθ. Therefore, cosθ = 0.49, which gives θ = 61° (approx). Therefore, the answer is B) 46°.

Question 12

The intensity of unpolarized light passing through a single sheet of polarizing material changes by a factor of: A)1. B)0.5. C)cos θ. D)cos² θ.

Accepted Answer

When unpolarized light passes through a single sheet of polarizing material, the intensity is reduced by a factor of 0.5 (or approximately 50%) because only half of the light waves are able to pass through the polarizing material in the direction of polarization. The other half of the light waves are blocked or absorbed by the polarizing material. The other answer choices have more complex and unnecessary equations that do not accurately describe the change in intensity for unpolarized light passing through a single sheet of polarizing material.

Question 13

At what angle is the Sun above the horizon if its light is found to be completely polarized when it is reflected from the top surface of a slab of glass (n = 1.48)?
A)34.0°
B)56.0°
C)0.594°
D)42.5°
E)47.5°

Accepted Answer

Brewster's angle is given by tan θ = n, where n is the index of refraction. For n = 1.48, θ = 34.0°.

Question 14

If the polarizing angle for diamond is 67.5°,what is the index of refraction of this material?
A)2.00
B)2.20
C)2.41
D)2.65

Accepted Answer

The polarizing angle for a material is given by the equation θp = tan^-1(n), where θp is the polarizing angle and n is the index of refraction. Therefore, we have n = tan(67.5°) = 2.41. The correct choice is (C).

Question 15

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 35.8° to that of polarizer 1.Polarizer 3 is placed after polarizer 2.Polarizer 3 has its plane of polarization at 58.8° to the plane of polarization of polarizer 2 and at 94.6° to that of polarizer 1.What fraction of the intensity of the original light gets though the last polarizer?
A)0.177
B)0.463
C)0.232
D)0.088
E)​0.021

Accepted Answer

The intensity of light after passing through each polarizer is given by Malus's law, I = I0 * cos^2(θ), where I0 is the initial intensity, and θ is the angle between the planes of polarization of the light and the polarizer. After passing through the first polarizer, the light is polarized, and its intensity is reduced by half (I1 = I0/2). After the second polarizer, the intensity is I2 = I1 * cos^2(35.8°). After the third polarizer, the intensity is I3 = I2 * cos^2(58.8°). However, the angle between polarizer 1 and 3 is given as 94.6°, which is not directly needed for the calculation since we're interested in the sequence of polarizations through the polarizers. The correct calculation involves only the angles between successive polarizers. Therefore, I3 = (I0/2) * cos^2(35.8°) * cos^2(58.8°) ≈ 0.088.

Question 16

The critical angle for sapphire surrounded by air is 34.4°.Calculate the polarizing angle for sapphire.
A)60.5°
B)59.7°
C)58.6°
D)56.3°

Accepted Answer

The polarizing angle is given by the equation tan(polarizing angle) = n, where n is the index of refraction of the material. For sapphire, n = 1.76, so tan(polarizing angle) = 1.76. Therefore, the polarizing angle is 60.5°.

Quiz 24: Wave Optics

Sunlight reflected from a smooth ice surface is completely polarized.Determine the angle of incidence.(n_ice = 1.309)

A material is optically active if it:

Why are sound waves not polarizable?

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 44.0° to that of polarizer 1.What fraction of the intensity of the original light gets though the second polarizer?

LCD stands for:

How far above the horizon is the Moon when its image reflected in calm water is completely polarized? (n_water = 1.333)

When the Sun is located near one of the horizons,an observer looking at the sky directly overhead will view partially polarized light.This effect is due to which of the following processes?

Polaroid sunglasses help when skiing on snow on a sunny day by reducing the sunlight from the snow.This light from the snow has been polarized by:

An unpolarized beam of light is incident on a pane of glass (n = 1.69) such that the reflected component coming off the glass is completely polarized.What is the angle of incidence in this case?

The blue light from the sky has been polarized by:

Unpolarized light of intensity I₀ passes through two sheets of ideal polarizing material.If the transmitted intensity is 0.24 I₀,what is the angle between the polarizer and the analyzer?

The intensity of unpolarized light passing through a single sheet of polarizing material changes by a factor of:

At what angle is the Sun above the horizon if its light is found to be completely polarized when it is reflected from the top surface of a slab of glass (n = 1.48) ?

If the polarizing angle for diamond is 67.5°,what is the index of refraction of this material?

The critical angle for sapphire surrounded by air is 34.4°.Calculate the polarizing angle for sapphire.