Question 1

If n_water = 1.50 and n_glass = 1.33, then total internal reflection at an interface between this glass and water: A) occurs whenever the light goes from glass to water B) occurs whenever the light goes from water to glass C) may occur when the light goes from glass to water D) may occur when the light goes from water to glass E) can never occur at this interface

Accepted Answer

Total internal reflection occurs when the angle of incidence is greater than the critical angle, which is given by sin(theta_c) = n2/n1, where n1 and n2 are the refractive indices of the two mediums. In this case, n1 is water and n2 is glass. Using this formula, the critical angle for glass-water interface is approximately 61 degrees. Therefore, total internal reflection may occur when light goes from water to glass at angles of incidence greater than 61 degrees.

Question 2

A ray of light passes through three media as shown. The speeds of light in these media obey: A) v₁ > v₂ > v₃ B) v₃ > v₂ > v₁ C) v₃ > v₁ > v₂ D) v₂ > v₁ > v₃ E) v₁ > v₃ > v₂

Accepted Answer

The speed of light is given by v = c/n where c is the speed of light in vacuum and n is the refractive index of the medium. As refractive index is inversely proportional to the speed of light, the medium with the highest refractive index will have the lowest speed of light. From the given values, we can see that v₃ has the highest refractive index and hence the lowest speed of light. Thus, option C is correct as it has v₃ > v₁ > v₂.

Question 3

If n_water = 1.33, what is the angle of refraction for the ray shown? A) 19$\degree$ B) 22$\degree$ C) 36$\degree$ D) 42$\degree$ E) 48$\degree$

Accepted Answer

According to Snell's Law, sin(angle of incidence)/sin(angle of refraction) = n1/n2, where n1 is the refractive index of the medium the ray is coming from and n2 is the refractive index of the medium the ray is entering. In this case, n1 = 1 (air) and n2 = 1.33 (water). Plugging in the given value, we get sin(angle of incidence)/sin(angle of refraction) = 1/1.33. Solving for angle of refraction, we get angle of refraction = arcsin(sin(angle of incidence)/1.33). The angle of incidence in the diagram appears to be around 50 degrees. Plugging this in, we get angle of refraction = arcsin(sin(50)/1.33) = 42 degrees (rounded to the nearest degree). Therefore, the correct answer is D.

Question 4

The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is: 
A) 0.53
B) 0.88
C) 1.9
D) 2.2
E) 3.0

Accepted Answer

The answer of The diagram shows the passage of a...

Question 5

When light travels from medium X to medium Y as shown: 
A) both the speed and the frequency decrease
B) both the speed and the frequency increase
C) both the speed and the wavelength decrease
D) both the speed and the wavelength increase
E) both the wavelength and the frequency are unchanged

Accepted Answer

When light travels from one medium to another, its speed and wavelength change. The speed of light in medium Y is lower than in medium X, causing the velocity of light to decrease, and the wavelength to decrease as well. The frequency is unaffected by the change in medium. Therefore, both the speed and the wavelength decrease, making option C the correct answer.

Question 6

As light goes from one medium to another, it is bent away from the normal. Then:
A) the speed of the light has increased
B) dispersion must occur
C) the second medium has a higher index of refraction
D) no change in speed has occurred
E) refraction has not occurred because refraction means a bending toward the normal

Accepted Answer

When light bends away from the normal as it passes from one medium to another, it indicates that the speed of light has increased in the second medium. This is because the light bends away from the normal when it moves into a less optically dense medium, where it travels faster.

Question 7

The index of refraction of a certain glass is 1.50. The sine of the critical angle for total internal reflection at a glass-air interface is:
A) 0.50
B) 0.67
C) 0.75
D) 1.00
E) 1.50

Accepted Answer

The critical angle θc is given by sin θc = n2/n1, where n1 and n2 are the indices of refraction of the two media. In this case, we are looking at a glass-air interface, so n1 = 1.00 and n2 = 1.50. Plugging in these values, we get sin θc = 1.50/1.00 = 1.50. However, the sine of an angle cannot be greater than 1, so this result is impossible. Therefore, we must use the fact that total internal reflection occurs when the incident angle is greater than the critical angle to conclude that sin θc < 1. The only answer choice that satisfies this condition is B, sin θc = 1.00/1.50 = 0.67.

Question 8

A pole stands in a river, half in and half out of the water. Another pole of the same length stands vertically on the shore at a place where the ground is level. The shadow cast by the pole in the river on the river bottom is:
A) slightly longer than the shadow of the pole on land
B) much longer than the shadow of the pole on land
C) shorter than the shadow of the pole on land
D) shorter than the shadow of the pole on land if the sun is high and longer if the sun is low
E) the same length as the shadow of the pole on land

Accepted Answer

The answer of A pole stands in a river, half...

Question 9

The rectangular metal tank shown is filled with an unknown liquid. The observer, whose eye is level with the top of the tank, can just see corner E. The index of refraction of this liquid is: 
A) 1.75
B) 1.67
C) 1.50
D) 1.33
E) 1.25

Accepted Answer

The answer of The rectangular metal tank shown is filled...

Question 10

The illustration shows total internal reflection taking place in apeice of glass. The index of refraction of this glass: 
A) at least 2.0
B) at most 2.0
C) at least 1.15
D) at most 1.15
E) cannot be calculated from the given data

Accepted Answer

The answer of The illustration shows total internal reflection taking...

Question 11

A ray of light in water (index n₁) is incident on its surface (with air) at the critical angle. Some oil (index n₂) is now floated on the water. The angle between the ray in the oil and the normal is: A) sin^-¹(1.00) B) sin^-¹(1/n₁) C) sin^-¹(1/n₂) D) sin^-¹(n₁/n₂) E) sin^-¹(n₂/n₁)

Accepted Answer

When a ray of light passes from a denser to a rarer medium, it bends away from the normal, and when it passes from a rarer to a denser medium, it bends towards the normal. At the critical angle, the angle of incidence is such that the angle of refraction is 90 degrees, and the refracted Ray grazes along the surface of the denser medium. This angle of incidence at the critical angle is different for different pairs of media. When the oil is floated on the water, the angle between the ray and the normal increases, which means that the angle of incidence in the oil is greater than the critical angle. Therefore, the ray undergoes total internal reflection at the oil-water interface. The angle between the reflected ray in oil and the normal is the same as the angle of incidence in oil. Using the relation of Snell's law, sin i1/sin r1 = n2/n1, where i1 is the angle of incidence, r1 is the angle of refraction, n1 is the refractive index of the denser medium, and n2 is the refractive index of the rarer medium. At the critical angle, sin r1 = 1. For the ray that is reflected in the oil, the denser medium is the oil, and the rarer medium is the air. Hence, sin i1/sin r1 = n/n_{2. Therefore, sin i1 = n}/n_2.

Question 12

The separation of white light into colors by a prism is associated with:
A) total internal reflection
B) partial reflection from each surface
C) variation of index of refraction with wavelength
D) a decrease in the speed of light in the glass
E) selective absorption of various colors

Accepted Answer

The separation of white light into colors by a prism is due to the variation of the index of refraction with wavelength, which is called dispersion. This causes different colors to bend at different angles as they pass through the prism, resulting in the observed spectrum of colors.

Question 13

The diagram shows total internal reflection. Which of the following statements is NOT true? 
A) angle AON is the angle of incidence
B) angle AON = angle BON
C) angle AON must be the critical angle
D) the speed of light in medium II is greater than that in medium I
E) if angle AON were increased, there would still be total internal reflection

Accepted Answer

The answer of The diagram shows total internal reflection. Which...

Question 14

The critical angle for total internal reflection at a diamond-air interface is 25$\degree$. Suppose light is incident at an angle of $\theta$ with the normal. Total internal reflection will occur if the incident medium is: A) air and $\theta$ = 25$\degree$ B) air and $\theta$ > 25$\degree$ C) air and $\theta$ < 25$\degree$ D) diamond and $\theta$ < 25$\degree$ E) diamond and $\theta$ > 25$\degree$

Accepted Answer

Total internal reflection occurs when light travels from a medium with a higher refractive index (diamond) to a medium with a lower refractive index (air) and the angle of incidence is greater than the critical angle.

Question 15

The index of refraction for diamond is 2.5. Which of the following is correct for the situation shown? 
A) (sin a)/(sin b) = 2.5
B) (sin b)/(sin d) = 2.5
C) (cos a)/(cos c) = 2.5
D) (sin a)/(sin c) = 1/(2.5)
E) a/c = 2.5

Accepted Answer

The formula that relates the angles and index of refraction for a material is given by: 
(sin i)/(sin r) = n
where i is the angle of incidence, r is the angle of refraction, and n is the index of refraction of the material.
In this situation, we have two angles of incidence (a and c) and one angle of refraction (b). So we can use the formula twice to get:
(sin a)/(sin b) = n  and  (sin c)/(sin b) = n
Dividing these two equations, we get:
(sin a)/(sin c) = n/n = 1
But we know that n = 2.5 for diamond, so we have:
(sin a)/(sin c) = 1/2.5
which simplifies to:
(sin a)/(sin c) = 0.4 
Therefore, the correct choice is D: (sin a)/(sin c) = 1/(2.5).

Question 16

Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass? 
A) I
B) II
C) III
D) IV
E) V

Accepted Answer

The answer of Which diagram below illustrates the path of...

Question 17

The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a benzene-air interface, is about:
A) 56$\degree$
B) 47$\degree$
C) 34$\degree$
D) 22$\degree$
E) 18$\degree$

Accepted Answer

The critical angle can be calculated using the formula: 
critical angle = sin⁻¹(n₂/n₁)
where n₁ is the index of refraction of the initial medium (in this case, benzene) and n₂ is the index of refraction of the final medium (in this case, air).
Plugging in the given values, we get:
critical angle = sin⁻¹(1/1.80) = 34.4°
So the closest answer choice is C, which is 34°.

Question 18

When light passes from air to glass, it bends:
A) toward the normal without changing speed
B) toward the normal and slows down
C) toward the normal and speeds up
D) away from the normal and slows down
E) away from the normal and speeds up

Accepted Answer

When light passes from air to glass, it bends toward the normal because light travels more slowly in glass than in air.

Question 19

A ray of light passes obliquely through a plate of glass having parallel faces. The emerging ray:
A) is totally internally reflected
B) is bent more toward the normal than the incident ray
C) is bent further away from the normal than the incident ray
D) is parallel to the incident ray but displaced sideways
E) lies on the same straight line as the incident ray

Accepted Answer

When a ray of light passes through a plate of glass with parallel faces, it emerges parallel to the incident ray but is displaced sideways due to refraction at both surfaces. The direction of the ray does not change; only its position does.

Quiz 33: Electromagnetic Waves

If n_water = 1.50 and n_glass = 1.33, then total internal reflection at an interface between this glass and water:

A ray of light passes through three media as shown. The speeds of light in these media obey:

If n_water = 1.33, what is the angle of refraction for the ray shown? $If n<sub>water</sub> = 1.33, what is the angle of refraction for the ray shown? A) 19 \degree B) 22 \degree C) 36 \degree D) 42 \degree E) 48 \degree$

The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is: $The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is: A) 0.53 B) 0.88 C) 1.9 D) 2.2 E) 3.0$

When light travels from medium X to medium Y as shown:

As light goes from one medium to another, it is bent away from the normal. Then:

The index of refraction of a certain glass is 1.50. The sine of the critical angle for total internal reflection at a glass-air interface is:

A pole stands in a river, half in and half out of the water. Another pole of the same length stands vertically on the shore at a place where the ground is level. The shadow cast by the pole in the river on the river bottom is:

A ray of light in water (index n₁) is incident on its surface (with air) at the critical angle. Some oil (index n₂) is now floated on the water. The angle between the ray in the oil and the normal is:

The separation of white light into colors by a prism is associated with:

The diagram shows total internal reflection. Which of the following statements is NOT true?

The critical angle for total internal reflection at a diamond-air interface is 25 $\degree$ . Suppose light is incident at an angle of $\theta$ with the normal. Total internal reflection will occur if the incident medium is:

Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass?

The index of refraction of benzene is 1.80. The critical angle for total internal reflection, at a benzene-air interface, is about:

When light passes from air to glass, it bends:

A ray of light passes obliquely through a plate of glass having parallel faces. The emerging ray:

Quiz 33: Electromagnetic Waves

If nwater = 1.50 and nglass = 1.33, then total internal reflection at an interface between this glass and water:

A ray of light passes through three media as shown. The speeds of light in these media obey:

If nwater = 1.33, what is the angle of refraction for the ray shown?

The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is: