Question 1

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 2

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 incident angle of light exceeds the critical angle, which is given by sinθc = n2/n1 (where n2 is the refractive index of the medium with lower refractive index and n1 is the refractive index of the medium with higher refractive index). Since the refractive index of water (n1) is higher than the refractive index of glass (n2), the critical angle for total internal reflection will be when light goes from water to glass. Therefore, total internal reflection may occur when the light goes from water to glass.

Question 3

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

The answer of The critical angle for total internal reflection...

Question 4

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 the light ray passes from water to oil, it bends away from the normal. Therefore, the angle between the incident ray and the normal (in the oil) is greater than the critical angle of water-air interface. The formula that relates the angles of incidence and refraction is Snell's law: n1sinθ1=n2sinθ2, where n1 and n2 are the refractive indices of the media on either side of the boundary, and θ1 and θ2 are the angles that the incident and refracted rays make with the normal, respectively. At the critical angle, sinθ2=1, so sinθ1=n2/n1. In this case, n1=1 (air) and n2=n₁ (water), so sinθ1=n₁/1=n₁. But when the light ray crosses the water-oil boundary, the refractive index changes to n₂. Thus, the angle between the refracted ray and the normal in oil is given by sinθ2=n1/n2 x sinθ1=1/n₂ x sinθ1=sinθ1/n₂=sin(^-¹)/n₂.

Question 5

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 is defined as the angle of incidence where the angle of refraction is 90 degrees. At this angle, the refracted ray travels along the boundary between the two media. The sine of the critical angle is given by:
sin(critical angle) = 1/n
where n is the index of refraction of the medium with the larger angle of incidence (in this case, the glass).
Plugging in the given value of n = 1.5, we get:
sin(critical angle) = 1/1.5
sin(critical angle) = 0.67
Therefore, the answer is B.

Question 6

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 7

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 is given by the formula $\sin^{-1}\left(\frac{n_2}{n_1}\right)$. In this case, $n_1$ is the index of refraction of benzene and $n_2$ is the index of refraction of air, which is approximately 1. The critical angle is therefore $\sin^{-1}(1/1.8) \approx 34^\circ$.

Question 8

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

Total internal reflection occurs when light travels from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence is greater than the critical angle.

In the illustration, the light is traveling from the glass to the air, which has a lower index of refraction. Therefore, the glass must have a higher index of refraction.

The critical angle is given by the equation sinθc = n2/n1, where θc is the critical angle, n1 is the index of refraction of the first medium (in this case, glass), and n2 is the index of refraction of the second medium (in this case, air).

We know that total internal reflection is occurring in the glass, which means that the angle of incidence is greater than the critical angle, so sinθ > sinθc.

This tells us that n2/n1 < 1, since sinθ = n2/n1 * sinθc, and sinθ is greater than sinθc.

Therefore, n1/n2 > 1, which means that the index of refraction of the glass is at least 1.15 (since that is the minimum value in the given answer choices). It could be larger than 1.15, but we cannot determine a specific value from the given data.

Question 9

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

The answer of If n_water = 1.33, what is the...

Question 10

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 answer of The index of refraction for diamond is...

Question 11

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 12

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 towards the normal and slows down. This is because the speed of light is slower in glass than in air due to the difference in the refractive index of the two materials.

Question 13

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 in a medium is given by v = c/n, where c is the speed of light in vacuum and n is the refractive index of the medium. From the given data, we have: v₁ = c/n1 v₂ = c/n2 v₃ = c/n3 Since n1 > n2 > n3, it follows that v₁ < v₂ < v₃. Therefore, choice C is the correct answer.

Question 14

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 15

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 index of refraction with wavelength. This property is called dispersion, and it causes each color of light to refract at a slightly different angle as it passes through the prism.

Question 16

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 17

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 angle of incidence is larger than the angle of refraction, which means that the ray of light is bending toward the normal as it passes into substance X. Therefore, the index of refraction of substance X must be greater than 1.0. Choice A and B are less than 1.0, so they are not possible. Choice E is too large and unlikely for most materials, leaving choices C and D. The angle of refraction is quite small, so we need a large index of refraction to explain the bending that occurs. Therefore, the best choice is C, 1.9.

Question 18

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 changes because different media have different refractive indices. The wavelength also changes because the speed of light is proportional to its wavelength. As the speed decreases, the wavelength decreases too. However, the frequency of the light remains constant because it is determined by the source that emits the light. Therefore, choice C is the correct answer.

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

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:

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

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 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 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:

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

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

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

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

When light passes from air to glass, it bends:

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

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

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:

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

Quiz 33: Electromagnetic Waves

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:

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

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