Question 1

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 2

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

Using Snell's Law at the first surface and geometry of the prism, the angle of refraction inside the prism is calculated. Then, using the prism's apex angle, the angle of incidence at the second surface is determined.

Question 3

A monochromatic light source emits a wavelength of 490 nm in air.When passing through a liquid,the wavelength reduces to 389 nm.What is the liquid's index of refraction?
A) 1.26
B) 1.33
C) 1.14
D) 1.49

Accepted Answer

The index of refraction (n) is calculated using the formula n = λ_air / λ_liquid. Substituting the given values, n = 490 nm / 389 nm = 1.26.

Question 4

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 5

A material has an index of refraction of 1.92 for light from a 560 nm source.What is the speed of light for this wavelength within the material? (c = 3.00 × 10⁸ m/s) A) 2.19 × 10⁸ m/s B) 4.68 × 10⁸ m/s C) 1.56 × 10⁸ m/s D) 1.92 × 10⁸ m/s

Accepted Answer

The answer of A material has an index of refraction...

Question 6

What is the angle of incidence on an air-to-glass boundary if the angle of refraction in the glass (n = 1.60)is 25°?
A) 40°
B) 25°
C) 43°
D) 16°

Accepted Answer

The angle of incidence can be calculated using the Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media:
sin(angle of incidence)/sin(25°) = 1/1.60
sin(angle of incidence) = sin(25°)/1.60
angle of incidence = arcsin(sin(25°)/1.60) ≈ 43°. Therefore, the best answer choice is C.

Question 7

A ray of light travels from a glass-to-liquid interface at an angle of 41.8°.Indices of refraction for the glass and liquid are,respectively,1.52 and 1.63.What is the angle of refraction for the ray moving through the liquid?
A) 23.2°
B) 46.0°
C) 32.3°
D) 38.4°

Accepted Answer

The answer of A ray of light travels from a...

Question 8

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

Accepted Answer

The answer of A beam of light is incident upon...

Question 9

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 angle of incidence is equal to the angle of refraction when the light exits the slab, due to the parallel sides of the slab. Thus, the angle of incidence is 67°.

Question 10

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 correct answer is A.The angle of refraction as the ray enters the air on the far side of the prism is 39.4°. This can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium. In this case, the first medium is glass and the second medium is air. The speed of light in glass is slower than the speed of light in air, so the angle of refraction will be greater than the angle of incidence.

Question 11

A fiber optic cable (n = 1.40)is submerged in water (n = 1.33).What is the critical angle for light to stay inside the cable?
A) 71.8°
B) 27.6°
C) 62.5°
D) 41.8°

Accepted Answer

The critical angle for total internal reflection can be calculated using the formula sinθc = n2/n1, where n2 is the refractive index of the first medium (water) and n1 is the refractive index of the second medium (fiber optic cable). Plugging in the values given, we get sinθc = 1.33/1.40, which yields θc = sin^-1(1.33/1.40) = 71.8°. Therefore, light entering the fiber optic cable at an angle greater than 71.8° will be reflected back into the cable.

Question 12

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

Using Snell's law at the air-to-oil interface, we find the angle of refraction in the oil. Then, applying Snell's law again at the oil-to-water interface, we calculate the incident angle at the oil-to-water surface, which is 26.0°.

Question 13

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 in air.What is the value of θ? 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, when light passes through multiple layers and returns to the original medium (air in this case), the angle of incidence is equal to the angle of refraction. Thus, θ = 40°.

Question 14

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

The answer of Light in air enters a diamond (n...

Question 15

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

Red light moves at the highest speed in the prism because it has the longest wavelength and is least refracted compared to other colors.

Question 16

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

Using Snell's Law at both interfaces, first calculate the angle of refraction in the oil using n_air * sin(40°) = n_oil * sin(θ_oil). Then, use Snell's Law again at the oil-water interface: n_oil * sin(θ_oil) = n_water * sin(θ_water). Solving these gives θ_water ≈ 28.8°.

Question 17

If light from a 560 nm monochromatic source in air is incident upon the surface of fused quartz (n = 1.56)at an angle of 70°,what is the wavelength of the ray refracted within the quartz?
A) 560 nm
B) 874 nm
C) 192 nm
D) 359 nm

Accepted Answer

The wavelength of light in a medium is given by λ_medium = λ_air / n. Here, λ_air = 560 nm and n = 1.56. So, λ_quartz = 560 nm / 1.56 ≈ 359 nm.

Question 18

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 19

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 20

If the wavelength of a monochromatic source is 600 nm in vacuum,what is the wavelength from the same source when it passes through a liquid where the speed of light is 2.00 × 10⁸ m/s? (c = 3.00 × 10⁸ m/s) A) 612.5 nm B) 671 nm C) 400 nm D) 392 nm

Accepted Answer

The wavelength in the liquid is given by λ' = λ * (v/c), where λ is the original wavelength, v is the speed of light in the liquid, and c is the speed of light in vacuum. Substituting the values, λ' = 600 nm * (2.00 × 10^8 m/s) / (3.00 × 10^8 m/s) = 400 nm.

Quiz 24: Wave Optics: Part A

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 monochromatic light source emits a wavelength of 490 nm in air.When passing through a liquid,the wavelength reduces to 389 nm.What is the liquid's index of refraction?

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 material has an index of refraction of 1.92 for light from a 560 nm source.What is the speed of light for this wavelength within the material? (c = 3.00 × 10⁸ m/s)

What is the angle of incidence on an air-to-glass boundary if the angle of refraction in the glass (n = 1.60) is 25°?

A ray of light travels from a glass-to-liquid interface at an angle of 41.8°.Indices of refraction for the glass and liquid are,respectively,1.52 and 1.63.What is the angle of refraction for the ray moving through the liquid?

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

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 fiber optic cable (n = 1.40) is submerged in water (n = 1.33) .What is the critical angle for light to stay inside the cable?

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?

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 in air.What is the value of θ?

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?

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

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?

If light from a 560 nm monochromatic source in air is incident upon the surface of fused quartz (n = 1.56) at an angle of 70°,what is the wavelength of the ray refracted within the quartz?

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 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?

If the wavelength of a monochromatic source is 600 nm in vacuum,what is the wavelength from the same source when it passes through a liquid where the speed of light is 2.00 × 10⁸ m/s? (c = 3.00 × 10⁸ m/s)