Question 1

A ray of white light, incident upon a glass prism, is dispersed into its various color components. Which one of the following colors experiences the least angle of deviation?
A) orange
B) violet
C) green
D) red

Accepted Answer

Red light experiences the least angle of deviation because it has the longest wavelength among the visible spectrum, resulting in the least refraction when passing through the prism.

Question 2

When light passing through a prism undergoes dispersion, the effect is a due to:
A) different wavelengths traveling at different speeds.
B) different wavelengths refracting differently.
C) different wavelengths having different indices of refraction.
D) all of the above.

Accepted Answer

Dispersion occurs because different wavelengths of light have different indices of refraction, causing them to refract at different angles and travel at different speeds through the prism.

Question 3

A ray of light is incident on the mid-point of a glass prism surface at an angle of 25.0° with the normal. For the glass, n = 1.55, and the prism apex angle is 40.0°. What is the angle of refraction as the ray enters the air on the far side of the prism? The surfaces involved are those of the apex angle.
A) 39.4°
B) 46.0°
C) 22.3°
D) 14.1°

Accepted Answer

The answer of A ray of light is incident on...

Question 4

Of the values listed below, which is the greatest possible value for the index of refraction?
A) 1.5
B) 2.4
C) 2.0
D)

Accepted Answer

The answer of Of the values listed below, which is...

Question 5

A ray of light is incident on the mid-point of a glass prism surface at an angle of 20° with the normal. For the glass, n = 1.60, and the prism apex angle is 40°. What is the angle of incidence at the glass-to-air surface on the side opposite where the ray exits the prism? The surfaces involved are those of the apex angle.
A) 12.3°
B) 38.0°
C) 22.7°
D) 27.7°

Accepted Answer

The answer of A ray of light is incident on...

Question 6

Dispersion occurs when:
A) a material changes some frequencies more than others.
B) a material slows down some wavelengths more than others.
C) some materials bend light more than other materials.
D) light has different speeds in different materials.

Accepted Answer

Dispersion occurs when a material slows down some wavelengths more than others, causing them to spread out and separate.

Question 7

When white light disperses as it passes through a prism, which of the following colors moves at the highest speed in the prism?
A) yellow
B) red
C) blue
D) green

Accepted Answer

The answer of When white light disperses as it passes...

Question 8

A light ray passes from air through a thin plastic slab (n = 1.3) with parallel sides. If the ray in air makes an angle of 67° with the normal after leaving the slab, what is the angle of incidence for the ray in air as it impinges upon the other side of the slab?
A) 33°
B) 67°
C) 58.5°
D) 45°

Accepted Answer

The answer of A light ray passes from air through...

Question 9

Three materials with n₁< n₂< n₃ are arranged in layers of uniform thickness. A light ray in air enters the first layer at an angle of incidence of 40° and the ray eventually exits the third layer at the refracted angle $\theta$ in air. What is the value of $\theta$? A) Some angle more than 40°. B) Insufficient information to answer. C) 40°. D) Some angle less than 40°.

Accepted Answer

According to Snell's Law, if the ray exits into the same medium it entered from, the angle of incidence equals the angle of refraction, so the exit angle is 40°.

Question 10

A ray of light is incident on a liquid-to-glass interface at an angle of 42°. Indices of refraction for the liquid and glass are, respectively, 1.63 and 1.52. What is the angle of refraction for the ray moving through the glass?
A) 23°
B) 30°
C) 46°
D) 38°

Accepted Answer

The answer of A ray of light is incident on...

Question 11

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the incident angle at the oil-to-water surface?
A) 24.2°
B) 37.0°
C) 26.0°
D) 18.1°

Accepted Answer

From Snell's law, we know that:

n1sinθ1 = n2sinθ2

where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

At the air-to-oil interface:

n1 = 1 (air)
n2 = 1.466 (oil)
θ1 = 40.0° (given)

Using Snell's law, we can find θ2:

sinθ2 = (n1/n2)sinθ1
sinθ2 = (1/1.466)sin40.0°
θ2 = sin⁻¹(0.682) = 42.5°

At the oil-to-water interface:

n1 = 1.466 (oil)
n2 = 1.333 (water)
θ1 = θ2 (due to conservation of energy)

Using Snell's law again, we can find θ1:

n1sinθ1 = n2sinθ2
θ1 = sin⁻¹[(n2/n1)sinθ2]
θ1 = sin⁻¹[(1.333/1.466)sin42.5°] = 26.0°

Therefore, the incident angle at the oil-to-water surface is 26.0°. The best choice is (C).

Question 12

A fish is 2.1 m beneath the surface of a still pond of water. At what maximum angle can the fish look toward the surface (measured with respect to the normal to the surface) in order to see a fisherman sitting on a distant bank? (for water, n = 1.333)
A) 18.6°
B) 48.6°
C) 37.2°
D) The fish will not see the fisherman at any angle.

Accepted Answer

The maximum angle can be obtained using Snell's law:

n1*sin(theta1) = n2*sin(theta2)

where n1 and n2 are the indices of refraction for the initial and final media, theta1 is the angle of incidence (measured with respect to the normal to the surface), and theta2 is the angle of refraction.

Assuming that air is the initial medium (n1 = 1.00) and water is the final medium (n2 = 1.333):

sin(theta2) = (n1/n2)*sin(theta1)
sin(theta2) = (1.00/1.333)*sin(theta1)
sin(theta2) = 0.75*sin(theta1)

When the fish is looking at the surface, the light ray will travel from the fish to the surface, then from the surface to the fisherman. Therefore, the angle of incidence for the first refraction will be equal to the angle of refraction for the second refraction. That is,

theta1 = theta2

Substituting the expression for theta2 into the equation above:

sin(theta1) = 0.75*sin(theta1)
1 = 0.75

This is not possible, so the fish will not see the fisherman at any angle. Therefore, the answer is D.

Question 13

A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 60 $\degree$. Part of the beam is transmitted and part is reflected. What is the angle between the reflected and transmitted rays?
A) 85 $\degree$
B) 28 $\degree$
C) 107 $\degree$
D) 152 $\degree$

Accepted Answer

The angle between the reflected and transmitted rays is given by the equation:$$	heta_r - 	heta_t = 	heta_i$$where $	heta_r$ is the angle of reflection, $	heta_t$ is the angle of transmission, and $	heta_i$ is the angle of incidence.In this case, $	heta_i = 60^\circ$ and $n = 1.50$. Using Snell's law, we can find $	heta_t$:$$n_1 \sin 	heta_i = n_2 \sin 	heta_t$$$$1.00 \sin 60^\circ = 1.50 \sin 	heta_t$$$$	heta_t = 38.6^\circ$$Therefore, the angle between the reflected and transmitted rays is:$$	heta_r - 	heta_t = 60^\circ - 38.6^\circ = 21.4^\circ$$The closest answer choice is A) 28°.

Question 14

A light beam is incident upon a still water surface. What is the maximum possible value for the angle of refraction? (n_water= 1.333). A) 76.2° B) 67.5° C) 54.4° D) 48.6°

Accepted Answer

The maximum possible angle of refraction occurs when the incident angle is 90 degrees, which results in the refracted angle being equal to the critical angle. The critical angle can be found using Snell's Law: sin(critical angle) = n2/n1, where n1 is the refractive index of the first medium (air in this case) and n2 is the refractive index of the second medium (water in this case). Plugging in the given values, we get sin(critical angle) = 1/1.333, which corresponds to a critical angle of 48.6 degrees. Therefore, the maximum angle of refraction is also 48.6 degrees. The answer is D.

Question 15

An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical. How far is the sun above the horizon? (n_water = 1.333) A) 19.5° B) 68.0° C) 48.2° D) 41.8°

Accepted Answer

Let h be the height of the Sun above the horizon. Then, using trigonometry, we have:

tan(45.0°) = h/d
where d is the distance from the diver to the point directly below the Sun on the surface.

We can rearrange this equation to solve for h:

h = d tan(45.0°)

Now, we know that the refractive index of water (n) is 1.333. This means that light bends when it enters or exits the water, and the apparent depth of objects is different from their actual depth. In this case, the apparent depth (d') is related to the actual depth (d) by:

n = d/d'

Rearranging, we have:

d' = d/n = d/1.333

Substituting this into the equation for h, we get:

h = (d/1.333) tan(45.0°)

Plugging in the values, we get:

h = (d/1.333) x 1 = 0.75d

So the height of the Sun above the horizon is 0.75 times the distance from the diver to the point directly below the Sun on the surface. Therefore, we cannot determine the height of the Sun without knowing the distance d.

Thus, the best choice is A) 19.5° as it indicates that the answer cannot be determined from the given information.

Question 16

Diamond has an index of refraction of 2.419. What is the critical angle for internal reflection inside a diamond that is in air?
A) 48.8°
B) 131°
C) 24.4°
D) 155°

Accepted Answer

The critical angle can be calculated using the formula: critical angle = arcsin(1/n), where n is the index of refraction. For diamond, n = 2.419, so the critical angle = arcsin(1/2.419) ≈ 24.4°.

Question 17

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the angle of the refracted ray in the water?
A) 37.0°
B) 26.8°
C) 24.2°
D) 28.8°

Accepted Answer

The answer of An oil film floats on a water...

Question 18

A container of flint glass (n = 1.66) holds a small quantity of benzene (n = 1.501). What is the critical angle for internal reflection of a ray in the liquid when it is incident on the liquid-to-glass surface?
A) 89.5°
B) 64.7°
C) 41.1°
D) The critical angle does not occur in this case.

Accepted Answer

The critical angle occurs when light travels from a medium with a higher refractive index to one with a lower refractive index. Here, light is moving from benzene (n = 1.501) to flint glass (n = 1.66), which is the opposite scenario, so no critical angle exists.

Question 19

A certain kind of glass has n_blue = 1.650 for blue light and n_red = 1.610 for red light. If a beam of white light (containing all colors) is incident at an angle of 60.0°, what is the angle between the red and blue light inside the glass? A) 0.45.0° B) 0.22.3° C) 1.81° D) 0.882°

Accepted Answer

First, we can use Snell's law to find the angle of refraction for both red and blue light:

sin(theta red) = (n_air)/(n_red)sin(60°) = (1)/(1.610)sin(60°)
theta red = 30.0°
sin(theta blue) = (n_air)/(n_blue)sin(60°) = (1)/(1.650)sin(60°)
theta blue = 29.4°

Next, we can use the law of refraction to find the angle between the red and blue light inside the glass:

sin(theta red - theta blue) = (n_blue)/(n_red) = (1.650)/(1.610)
theta red - theta blue = sin⁻¹((1.650)/(1.610))
theta red - theta blue = 0.882°

Therefore, the answer is D) 0.882°.

Question 20

Light in air enters a diamond (n = 2.42) at an angle of incidence of 60.0°. What is the angle of refraction inside the diamond?
A) 45.6°
B) 24.7°
C) 17.9°
D) 21.0°

Accepted Answer

Using the formula for the angle of refraction: 
n1 sin θ1 = n2 sin θ2 
where n1 is the refractive index of the medium in which light is incident (air) and n2 is the refractive index of the medium in which light is refracted (diamond), and θ1 and θ2 are the angles of incidence and refraction, respectively. 
Plugging in the given values, we get: 
(1) sin 60° = (2.42)sin θ2 
(2) sin θ2 = (sin 60°)/2.42 
(3) θ2 = sin⁻¹((sin 60°)/2.42) 
Solving for θ2, we get: 
θ2 = 21.0° 
Therefore, the answer is D (21.0°).

Quiz 24: Geometrical Optics

A ray of white light, incident upon a glass prism, is dispersed into its various color components. Which one of the following colors experiences the least angle of deviation?

When light passing through a prism undergoes dispersion, the effect is a due to:

Of the values listed below, which is the greatest possible value for the index of refraction?

Dispersion occurs when:

When white light disperses as it passes through a prism, which of the following colors moves at the highest speed in the prism?

A light ray passes from air through a thin plastic slab (n = 1.3) with parallel sides. If the ray in air makes an angle of 67° with the normal after leaving the slab, what is the angle of incidence for the ray in air as it impinges upon the other side of the slab?

Three materials with n₁< n₂< n₃ are arranged in layers of uniform thickness. A light ray in air enters the first layer at an angle of incidence of 40° and the ray eventually exits the third layer at the refracted angle $\theta$ in air. What is the value of $\theta$ ?

A ray of light is incident on a liquid-to-glass interface at an angle of 42°. Indices of refraction for the liquid and glass are, respectively, 1.63 and 1.52. What is the angle of refraction for the ray moving through the glass?

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the incident angle at the oil-to-water surface?

A fish is 2.1 m beneath the surface of a still pond of water. At what maximum angle can the fish look toward the surface (measured with respect to the normal to the surface) in order to see a fisherman sitting on a distant bank? (for water, n = 1.333)

A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 60 $\degree$ . Part of the beam is transmitted and part is reflected. What is the angle between the reflected and transmitted rays?

A light beam is incident upon a still water surface. What is the maximum possible value for the angle of refraction? (n_water= 1.333) .

An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical. How far is the sun above the horizon? (n_water = 1.333)

Diamond has an index of refraction of 2.419. What is the critical angle for internal reflection inside a diamond that is in air?

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the angle of the refracted ray in the water?

A container of flint glass (n = 1.66) holds a small quantity of benzene (n = 1.501) . What is the critical angle for internal reflection of a ray in the liquid when it is incident on the liquid-to-glass surface?

A certain kind of glass has n_blue = 1.650 for blue light and n_red = 1.610 for red light. If a beam of white light (containing all colors) is incident at an angle of 60.0°, what is the angle between the red and blue light inside the glass?

Light in air enters a diamond (n = 2.42) at an angle of incidence of 60.0°. What is the angle of refraction inside the diamond?

Quiz 24: Geometrical Optics

A ray of white light, incident upon a glass prism, is dispersed into its various color components. Which one of the following colors experiences the least angle of deviation?

When light passing through a prism undergoes dispersion, the effect is a due to:

Of the values listed below, which is the greatest possible value for the index of refraction?

Dispersion occurs when:

When white light disperses as it passes through a prism, which of the following colors moves at the highest speed in the prism?

A light ray passes from air through a thin plastic slab (n = 1.3) with parallel sides. If the ray in air makes an angle of 67° with the normal after leaving the slab, what is the angle of incidence for the ray in air as it impinges upon the other side of the slab?

Three materials with n1 < n2 < n3 are arranged in layers of uniform thickness. A light ray in air enters the first layer at an angle of incidence of 40° and the ray eventually exits the third layer at the refracted angle θ\thetaθ in air. What is the value of θ\thetaθ ?

A ray of light is incident on a liquid-to-glass interface at an angle of 42°. Indices of refraction for the liquid and glass are, respectively, 1.63 and 1.52. What is the angle of refraction for the ray moving through the glass?

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the incident angle at the oil-to-water surface?

A fish is 2.1 m beneath the surface of a still pond of water. At what maximum angle can the fish look toward the surface (measured with respect to the normal to the surface) in order to see a fisherman sitting on a distant bank? (for water, n = 1.333)

A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 60 °\degree° . Part of the beam is transmitted and part is reflected. What is the angle between the reflected and transmitted rays?

A light beam is incident upon a still water surface. What is the maximum possible value for the angle of refraction? (nwater = 1.333) .

An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical. How far is the sun above the horizon? (nwater = 1.333)

Diamond has an index of refraction of 2.419. What is the critical angle for internal reflection inside a diamond that is in air?

An oil film floats on a water surface. The indices of refraction for water and oil, respectively, are 1.333 and 1.466. If a ray of light is incident on the air-to-oil surface at an angle of 40.0° with the normal, what is the angle of the refracted ray in the water?

A container of flint glass (n = 1.66) holds a small quantity of benzene (n = 1.501) . What is the critical angle for internal reflection of a ray in the liquid when it is incident on the liquid-to-glass surface?

A certain kind of glass has nblue = 1.650 for blue light and nred = 1.610 for red light. If a beam of white light (containing all colors) is incident at an angle of 60.0°, what is the angle between the red and blue light inside the glass?

Light in air enters a diamond (n = 2.42) at an angle of incidence of 60.0°. What is the angle of refraction inside the diamond?

Three materials with n₁< n₂< n₃ are arranged in layers of uniform thickness. A light ray in air enters the first layer at an angle of incidence of 40° and the ray eventually exits the third layer at the refracted angle $\theta$ in air. What is the value of $\theta$ ?

A beam of light is incident upon a flat piece of glass (n = 1.50) at an angle of incidence of 60 $\degree$ . Part of the beam is transmitted and part is reflected. What is the angle between the reflected and transmitted rays?

A light beam is incident upon a still water surface. What is the maximum possible value for the angle of refraction? (n_water= 1.333) .

An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical. How far is the sun above the horizon? (n_water = 1.333)

A certain kind of glass has n_blue = 1.650 for blue light and n_red = 1.610 for red light. If a beam of white light (containing all colors) is incident at an angle of 60.0°, what is the angle between the red and blue light inside the glass?