Question 1

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.

Question 2

A wavelength of 465 nm yields a first order maximum at 26.6° with a grating.At what angle will the third order maximum appear for this wavelength?
A) 13°
B) 90°
C) -26.6°
D) No third order maximum exists in this case.
E) ​1.50°

Accepted Answer

The third order maximum would require an angle that satisfies the grating equation for m=3. However, the sine of the angle would exceed 1, which is not possible, indicating no third order maximum exists.

Question 3

A beam of polarized light of intensity I₀ passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 10°.What is the intensity of the emerging light? A) 0.98 I₀ B) 0.97 I₀ C) 0.70 I₀ D) 1.00 I₀ E) 0.84 I₀

Accepted Answer

When a polarized beam of intensity I₀ passes through an ideal polarizing material whose transmission axis does not coincide with the polarization direction of the beam, the intensity of the beam decreases to (cosθ)² × I₀, where θ is the angle between the polarization direction of the beam and the transmission axis of the polarizing material. In this case, θ = 10°, so the intensity of the emerging light is: (cos10°)² × I₀ ≈ 0.97 I₀ Therefore, the correct choice is B.

Question 4

Polarization of light can be achieved using a dichroic material like Polaroid by which of the following processes?
A) reflection
B) double refraction
C) selective absorption
D) scattering

Accepted Answer

Dichroic materials like Polaroid selectively absorb light waves that are polarized in a specific direction. This process reduces the intensity of non-polarized and differently polarized light waves, allowing polarized light to pass through.

Question 5

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 answer of The critical angle for sapphire surrounded by...

Question 6

Unpolarized light of intensity I₀ passes through two sheets of ideal polarizing material.If the transmitted intensity is 0.33 I₀,what is the angle between the polarizer and the analyzer? A) 55° B) 36° C) 49° D) 71° E) 0.62°

Accepted Answer

The answer of Unpolarized light of intensity I₀ passes through...

Question 7

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 8

A diffraction grating has 6000 lines/cm.What is the slit separation?
A) 6.0 μm
B) 1.7 μm
C) 167 nm
D) 600 nm
E) ​Not enough information

Accepted Answer

Slit separation = 1/(number of lines per unit length) = 1/(6000 lines/cm) = 1.7 μm.

Question 9

A beam of unpolarized light in air strikes a flat piece of glass at an angle of incidence of 51.6°.If the reflected beam is completely polarized,what is the index of refraction of the glass?
A) 1.59
B) 1.26
C) 1.61
D) 1.47
E) ​1.90

Accepted Answer

The answer of A beam of unpolarized light in air...

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

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, its intensity reduces to half. This happens because the polarizing material allows only the light waves oscillating in one direction (parallel to its axis) to pass through while blocking the waves oscillating perpendicular to its axis, resulting in a reduction of intensity by a factor of 2.

Question 12

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 reflected and polarized in different directions, making it difficult to see and causing glare. Polaroid sunglasses are specifically designed to block out this reflected, polarized light, which improves visibility and reduces eye strain.

Question 13

An unpolarized beam of light is incident on a pane of glass (n = 1.36)such that the reflected component coming off the glass is completely polarized.What is the angle of incidence in this case?
A) 42.7°
B) 6.53°
C) 0.94°
D) 53.7°
E) ​47.4°

Accepted Answer

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

Question 14

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 39.8° to that of polarizer 1.Polarizer 3 is placed after polarizer 2.Polarizer 3 has its plane of polarization at 30.8° to the plane of polarization of polarizer 2 and at 70.6° to that of polarizer 1.What fraction of the intensity of the original light gets though the last polarizer?
A) 0.436
B) 0.664
C) 0.332
D) 0.218
E) ​0.085

Accepted Answer

The intensity of light after passing through multiple polarizers is given by Malus's Law. After the first polarizer, the intensity is halved. After the second polarizer, the intensity is reduced by cos²(39.8°). After the third polarizer, the intensity is further reduced by cos²(30.8°). Calculating these gives approximately 0.218 of the original intensity.

Question 15

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 near one of the horizons, its light has to pass through more atmosphere to reach the observer. This causes the light to scatter, which creates partially polarized light.

Question 16

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 30.7° to that of polarizer 1.What fraction of the intensity of the original light gets though the second polarizer?
A) 0.430
B) 0.740
C) 0.370
D) 0.860
E) ​0.285

Accepted Answer

The fraction of intensity that gets through the second polarizer is given by Malus' law: I = I₀cos²θ, where I₀ is the original intensity and θ is the angle between the planes of polarization of the two polarizers. Here, θ = 30.7°. Thus, I = I₀cos²30.7° = 0.370I₀. Therefore, the fraction of intensity that gets through the second polarizer is 0.370.

Question 17

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 is given by the equation tan θ = n, where θ is the polarizing angle and n is the index of refraction. Plugging in the given angle of 67.5°, we get tan 67.5° = 2.41, so the index of refraction of diamond is 2.41. Therefore, the best choice is C.

Question 18

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 answer of How far above the horizon is the...

Question 19

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 = 1.63)?
A) 31.5°
B) 58.5°
C) 0.55°
D) 37.8°
E) ​52.2°

Accepted Answer

The correct answer is A.The angle of incidence for complete polarization is given by Brewster's angle, which is given by the equation tan(theta_B) = n, where theta_B is the Brewster's angle and n is the refractive index of the medium. For glass with n = 1.63, we have tan(theta_B) = 1.63, which gives theta_B = 31.5 degrees.

Question 20

At what angle will the sixth order maximum occur for a wavelength of 447 nm using a diffraction grating with 7,250 lines per cm?
A) 30°
B) 90°
C) No sixth order maximum will occur in this case.
D) 1.57°
E) ​11.1°

Accepted Answer

The diffraction grating equation is d*sin(θ) = m*λ, where d is the distance between lines (1/7250 cm), m is the order number, and λ is the wavelength. For the sixth order (m=6), if sin(θ) exceeds 1, no maximum occurs. Calculating for m=6, sin(θ) > 1, so no sixth order maximum occurs.

Quiz 24: Wave Optics

A material is optically active if it:

A wavelength of 465 nm yields a first order maximum at 26.6° with a grating.At what angle will the third order maximum appear for this wavelength?

A beam of polarized light of intensity I₀ passes through a sheet of ideal polarizing material.The polarization axis of the beam and the transmission axis of the sheet differ by 10°.What is the intensity of the emerging light?

Polarization of light can be achieved using a dichroic material like Polaroid by which of the following processes?

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

Unpolarized light of intensity I₀ passes through two sheets of ideal polarizing material.If the transmitted intensity is 0.33 I₀,what is the angle between the polarizer and the analyzer?

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

A diffraction grating has 6000 lines/cm.What is the slit separation?

A beam of unpolarized light in air strikes a flat piece of glass at an angle of incidence of 51.6°.If the reflected beam is completely polarized,what is the index of refraction of the glass?

The blue light from the sky has been polarized by:

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

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 = 1.36) such that the reflected component coming off the glass is completely polarized.What is the angle of incidence in this case?

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?

Unpolarized light is passed through polarizer 1.The light then goes though polarizer 2 with its plane of polarization at 30.7° to that of polarizer 1.What fraction of the intensity of the original light gets though the second polarizer?

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

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

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 = 1.63) ?

At what angle will the sixth order maximum occur for a wavelength of 447 nm using a diffraction grating with 7,250 lines per cm?