Question 1

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.

Accepted Answer

Calcite has different indices of refraction for the two beams, causing them to refract differently and create two distinct images of the same object. This phenomenon is known as double refraction or birefringence. The other options are incorrect as they do not relate to the specific optical property of calcite known as double refraction.

Question 2

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

Accepted Answer

For light reflected from a non-conducting surface (like the surface of a lake), the angle of incidence at which light is 100% polarized is given by Brewster's Law: tanθp = n, where θp is the polarizing angle and n is the refractive index of the medium the light is entering from. 
Plugging in n = 1.33 (the refractive index of water) gives us tanθp = 1.33, which gives us θp ≈ 53º. 
Therefore, the correct choice is A).

Question 3

A 60° 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°
B) 18.9°
C) 29.4°
D) 30.6°
E) 60.6°

Accepted Answer

When light enters the prism at an angle of incidence $i$, it bends towards the normal by an angle of refraction $r$, given by Snell’s Law:

$n_{1}sin\:i=n_{2}sin\:r$

where $n_{1}$ is the refractive index of the medium outside the prism (usually air), and $n_{2}$ is the refractive index of the prism.

At the second face of the prism, the ray meets the boundary between the prism and air at an angle of incidence of $r$, and is refracted back into the prism at an angle of refraction $i$, again given by Snell’s Law. Total internal reflection occurs when there is no angle of refraction possible in the lower refractive index medium.

For the critical angle $	heta_{c}$, the angle of refraction $r$ is $90°$. Applying Snell’s Law gives:

$i=sin^{-1}\:\left(\frac{n_{2}}{n_{1}}ight)sin\:90°=sin^{-1}\left(\frac{n_{2}}{n_{1}}ight)$

Therefore:

$i=sin^{-1}\left(\frac{1.52}{1}\:sin\:60°\:ight)\approx29.4°$

Choice C is the correct answer.

Question 4

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.

Accepted Answer

The answer of The index of refraction of plate glass...

Question 5

White light is incident on a prism from the left. After it passes through the first prism, a color spectrum of light is observed. The spectrum is then passed through a second prism, which is inverted compared to the first prism. The color light that exits from the second prism
A) is also a color spectrum and more spread out.
B) is also a color spectrum but less spread out.
C) is white in color.
D) has more colors than the first spectrum.
E) has fewer colors than the first spectrum.

Accepted Answer

The answer of  White light is incident on a...

Question 6

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.

Accepted Answer

Plane polarized light has a fixed direction of polarization and the electric and magnetic fields oscillate perpendicular to each other and the direction of propagation. Therefore, 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.

Question 7

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.

Accepted Answer

Polarization of light can be achieved through methods such as selective absorption (polaroid filters), reflection (Brewster's angle), scattering (Rayleigh scattering), and double refraction (birefringence). However, simply passing light through a narrow slit does not polarize light; it mainly affects the light's diffraction pattern.

Question 8

A 60° 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° to the normal.
A) 24.3°
B) 35.8°
C) 45.1°
D) 48.7°
E) 55.3°

Accepted Answer

The answer of A 60° prism has a refractive index...

Question 9

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 θ_m, where θ_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.

Accepted Answer

The answer of  A fiber optic is made by...

Question 10

A 60° 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°
B) 1.5°
C) 3.2°
D) 2.4°
E) 0.4°

Accepted Answer

The critical angle for total internal reflection is different for blue and red light due to their different refractive indices. Calculating the critical angles and using Snell's law, the difference in the angle of incidence is approximately 2.4°.

Question 11

In any wave motion, dependence of velocity on wavelength is called
A) polarization.
B) deviation.
C) dispersion.
D) diffraction.
E) scattering.

Accepted Answer

The dependence of velocity on wavelength is called dispersion. This phenomenon is commonly observed in waves such as light and sound, where different wavelengths travel at different velocities through a medium. This results in the separation of colors in a rainbow and the distortion of sound waves in music played through a speaker.

Question 12

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

Accepted Answer

Diffraction is not a phenomenon by which polarized light can be produced from unpolarized light. The other four phenomena can lead to polarization of light.

Question 13

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.

Accepted Answer

The index of refraction of a sample of glass can be determined by measuring Brewster's angle, critical angle, angle of minimum deviation, and the ratio of true to apparent depth. However, the angle of dispersion between red and violet light is related to the material's dispersion (variation of refractive index with wavelength) rather than its absolute index of refraction.

Question 14

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° 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 vred)-vblue) ) * 100 / vred)?
A) 1.1%
B) 1.8%
C) 0.53%
D) The speed is the same for both colors.
E) 0.019%

Accepted Answer

The answer of The dependence of the index of refraction...

Question 15

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

Accepted Answer

The answer of Light known to be polarized in the...

Question 16

A 60° 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 light and a beam of blue light that are both incident at an angle of 60⁰. A) 0.4° B) 0.0° C) 1.3° D) 3.9° E) 2.7°

Accepted Answer

The angle of deviation depends on the refractive index and the angle of incidence. The difference in refractive indices for blue and red light causes a difference in deviation angles. Calculating using the prism formula and Snell's law, the difference in the angle of emergence is approximately 2.7°.

Question 17

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° 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°
B) 0.40°
C) 0.56°
D) 0.74°
E) 0.13°

Accepted Answer

The answer of The dependence of the index of refraction...

Question 18

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.

Accepted Answer

The angle of incidence for maximum polarization by reflection from a medium with index of refraction n is given by the equation θ=arctan(n). Plugging in the index of refraction of water, we get θ=arctan(1.33)≈53º. Therefore, the best choice is B.

Question 19

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°.
D) at 45°.
E) in any direction.

Accepted Answer

The polarizing axis should be vertical to reduce glare from horizontal surfaces like water, as reflected light is typically horizontally polarized.

Question 20

Two polarizers have their transmission axes at an angle θ. 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 cos²θ B) 0.5I cos² θ C) 0.25I cos² θ D) I cos θ E) 0.25I cos θ

Accepted Answer

The intensity of the light transmitted by the first polarizer is Icos²θ (Malus' law). The transmitted light is then incident on the second polarizer, so the intensity of the light transmitted by both polarizers is Icos²θcos²θ=Icos⁴θ. Therefore, the intensity of the light transmitted by the second polarizer is (1/2)Icos⁴θ (since the original intensity I is divided equally between the two polarizers). Simplifying this expression, we get 0.5Icos²θ(1+cos²θ)=0.5Icos²θ(1+cos²θ)=0.5Icos²θ²θ, which is the same as choice B.

Quiz 23: Wave Properties of Light

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

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 60° 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.

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

White light is incident on a prism from the left. After it passes through the first prism, a color spectrum of light is observed. The spectrum is then passed through a second prism, which is inverted compared to the first prism. The color light that exits from the second prism

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

One would not attempt to polarize light by

A 60° 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° to the normal.

A 60° 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.

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

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

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

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 60° 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 light and a beam of blue light that are both incident at an angle of 60⁰.

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

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

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