Question 1

What is the frequency of light that has a wavelength in water of 788 nm if the refractive index for this light is 1.33?
A)3.76 × 10¹⁴ Hz
B)5.00 × 10¹⁴ Hz
C)6.65 × 10¹⁴ Hz
D)2.86 × 10¹⁴ Hz
E)9.52 × 10¹⁴ Hz

Accepted Answer

D

Question 2

A fish swims 2.00 m below the surface of a pond.At what apparent depth does the fish appear to swim if viewed from directly above? The index of refraction of water is 1.33.
A)1.33 m
B)1.50 m
C)2.00 m
D)2.66 m
E)3.00 m

Accepted Answer

The apparent depth of the fish is given by the formula:
Apparent depth = Actual depth / Refractive index of the medium
In this case, the actual depth is 2.00 m and the refractive index of water is 1.33. Therefore, the apparent depth of the fish is:
Apparent depth = 2.00 m / 1.33 = 1.50 m
Hence, the fish appears to swim at a depth of 1.50 m when viewed from directly above. Thus, the best choice is (B).

Question 3

A beam of light passes from air into water.Which is necessarily true?
A)The frequency is unchanged and the wavelength increases.
B)The frequency is unchanged and the wavelength decreases.
C)The wavelength is unchanged and the frequency decreases.
D)Both the wavelength and frequency increase.
E)Both the wavelength and frequency decrease.

Accepted Answer

When a beam of light passes from air into water, the speed of light decreases. According to the equation v = fλ, if the speed (v) decreases and the frequency (f) remains constant, then the wavelength (λ) must also decrease. Therefore, the correct option is B - the frequency is unchanged and the wavelength decreases.

Question 4

The figure shows the path of a ray of light as it travels through air and crosses a boundary into water.The index of refraction of water for this light is 1.33.
 
-What is the angle of refraction for this situation?
A)0.37°
B)0.65°
C)22°
D)41°
E)60°

Accepted Answer

The answer of The figure shows the path of a...

Question 5

Light with a wavelength of 589 nm in a vacuum strikes the surface of an unknown liquid at an angle of 31.2° with respect to the normal to the surface.If the light travels at a speed of 1.97 × 10⁸ m/s through the liquid,what is the angle of refraction?
A)19.9°
B)26.1°
C)34.2°
D)39.3°
E)51.9°

Accepted Answer

To find the angle of refraction, we use Snell's Law, which is $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the refractive indices of the first and second mediums respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively. The refractive index of a medium is given by $n = \frac{c}{v}$, where $c$ is the speed of light in vacuum (approximately $3.00 \times 10^8$ m/s) and $v$ is the speed of light in the medium.Given that the light travels at a speed of $1.97 \times 10^8$ m/s through the liquid, the refractive index of the liquid is $n_2 = \frac{3.00 \times 10^8}{1.97 \times 10^8} \approx 1.52$. The refractive index of vacuum ($n_1$) is 1, and the angle of incidence ($\theta_1$) is 31.2°.Substituting these values into Snell's Law gives us $1 \times \sin(31.2°) = 1.52 \times \sin(\theta_2)$. Solving for $\theta_2$ gives us an angle of refraction of approximately 19.9°.

Question 6

When certain light rays pass from a vacuum into a block of an unknown material,the measured index of refraction of the material is 3.00.What is the speed of light inside the block?
A)9.9 × 10⁶ m/s
B)4.8 × 10⁷ m/s
C)1.0 × 10⁸ m/s
D)1.9 × 10⁸ m/s
E)2.9 × 10⁸ m/s

Accepted Answer

The speed of light in a material is given by the formula: speed of light in vacuum (c) divided by the index of refraction (n). Here, c = 3.0 × 10⁸ m/s and n = 3.00, so the speed of light in the material is (3.0 × 10⁸ m/s) / 3.00 = 1.0 × 10⁸ m/s.

Question 7

The figure shows the path of a portion of a ray of light as it passes through three different materials. Note: The figure is drawn to scale. What can be concluded concerning the refractive indices of these three materials? A)n₁ < n₂ < n₃ B)n₁ > n₂ > n₃ C)n₃ < n₁ < n₂ D)n₂ < n₁ < n₃ E)n₁ < n₃ < n₂

Accepted Answer

The ray of light bends away from the normal as it enters material 2 and bends towards the normal as it enters material 3. This indicates that material 2 has a higher refractive index than material 1, and material 3 has a higher refractive index than material 2. Therefore, the refractive indices are ordered from lowest to highest as n₃ < n₁ < n₂.

Question 8

The table lists the index of refraction for various substances at 20 °C for light with a wavelength of 589 nm in a vacuum.Through which substance will light with a vacuum wavelength of 589 nm travel with the greatest speed? 
A)fused quartz
B)crown glass
C)ethyl alcohol
D)carbon tetrachloride
E)crystalline quartz

Accepted Answer

The answer of The table lists the index of refraction...

Question 9

A grizzly bear is sitting on a rock in the middle of a calm river when she observes a fish directly below.If the apparent depth of the fish is 0.40 m,what is the actual depth at which the fish is swimming? The index of refraction of water is 1.33.
A)0.80 m
B)0.71 m
C)0.62 m
D)0.53 m
E)0.45 m

Accepted Answer

The answer of A grizzly bear is sitting on a...

Question 10

Complete the following statement: Fiber optics make use of
A)total internal reflection.
B)polarization.
C)chromatic aberration.
D)Brewster's angle.
E)dispersion.

Accepted Answer

Fiber optics make use of total internal reflection, where light reflects off the walls of the fiber, allowing it to be transmitted over long distances without significant loss. Polarization, chromatic aberration, Brewster's angle, and dispersion are all phenomena that can affect light waves, but they are not the main principles behind fiber optics.

Question 11

The figure shows the path of a ray of light as it travels through air and crosses a boundary into water.The index of refraction of water for this light is 1.33.
 
-What is the speed of this ray of light as it travels through the water?
A)1.54 × 10⁸ m/s
B)2.26 × 10⁸ m/s
C)2.86 × 10⁸ m/s
D)3.99 × 10⁸ m/s
E)4.43 × 10⁹ m/s

Accepted Answer

The speed of light in a vacuum is approximately 3.0 × 10⁸ m/s. The speed of light in a medium is given by v = c/n, where c is the speed of light in a vacuum and n is the refractive index of the medium. In this case, the refractive index of water is 1.33. Therefore, the speed of light in water is:
v = c/n = (3.0 × 10⁸ m/s) / 1.33 = 2.26 × 10⁸ m/s. Thus, the best choice is (B).

Question 12

A ray of light originates in medium A and is incident upon medium B.For which one of the following pairs of indices of refraction for A and B is total internal reflection not possible?

Accepted Answer

The answer of A ray of light originates in medium...

Question 13

The bending of light as it moves from one medium to another with differing indices of refraction is due to a change in what property of the light?
A)amplitude
B)period
C)frequency
D)speed
E)color

Accepted Answer

The bending of light, also known as refraction, occurs due to a change in the speed of light as it moves from one medium to another. This change in speed is caused by a change in the density of the medium, which is reflected by its index of refraction. As the speed of light changes, its direction is also altered, resulting in the bending of the light ray. Therefore, the correct answer is D) speed.

Question 14

A ray of light propagates in water (n = 1.333)and strikes a sheet of crown glass (n = 1.523).If the angle of refraction in the glass is 35.2°,determine the angle of incidence.
A)30.3°
B)32.8°
C)35.2°
D)41.2°
E)45.0°

Accepted Answer

Using Snell's Law, n1 * sin(θ1) = n2 * sin(θ2), where n1 = 1.333, n2 = 1.523, and θ2 = 35.2°. Solving for θ1 gives approximately 41.2°.

Question 15

Which one of the following expressions determines the critical angle for quartz (n = 1.5)immersed in oil (n = 1.1)?
A) = 1.5/1.1
B)= sin-¹ (1.1/1.5)
C) = sin (1.1/1.5)
D) = tan-¹ (1.1/1.5)

Accepted Answer

The critical angle between two mediums is given by sin-¹(n2/n1), where n1 is the refractive index of the first medium (in this case, quartz) and n2 is the refractive index of the second medium (in this case, oil). Therefore, the critical angle for quartz immersed in oil is sin-¹(1.1/1.5).

Question 16

Which one of the following statements concerning the index of refraction for a given material is true?
A)The index of refraction may be less than 1.
B)The index of refraction may be measured in nanometers.
C)The index of refraction does not depend on the frequency of the incident light.
D)For a given frequency,the index of refraction is inversely proportional to the wavelength of light in vacuum.
E)For a given frequency,the index of refraction is inversely proportional to the wavelength of light in the material.

Accepted Answer

The index of refraction for a given material is defined as the ratio of the speed of light in vacuum to the speed of light in the material. It is dependent on the wavelength/frequency of the incident light and determines how much the light bends when passing through the material. The correct statement is that for a given frequency, the index of refraction is inversely proportional to the wavelength of light in the material. Therefore, choice E is the correct answer. Choices A and B are incorrect as the index of refraction is always greater than or equal to 1, and is a unitless quantity. Choice C is incorrect as the index of refraction is frequency-dependent. Choice D is incorrect as the index of refraction is inversely proportional to the wavelength of light in the material, not in vacuum.

Question 17

A ray of light passes from air into a block of glass with a refractive index of 1.59 as shown in the figure. Note: The drawing is not to scale.
 What is the value of the distance D?
A)1.42 cm
B)1.66 cm
C)1.93 cm
D)2.19 cm
E)2.38 cm

Accepted Answer

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

Question 18

A scuba diver shines a flashlight from beneath the surface of water (n = 1.33)such that the light strikes the water-air boundary with an angle of incidence of 37°.At what angle is the beam refracted?
A)31°
B)53°
C)48°
D)65°
E)90°

Accepted Answer

Using Snell's Law: 
n1sinθ1 = n2sinθ2 
where n1 is the refractive index of the initial medium (water), θ1 is the angle of incidence, n2 is the refractive index of the second medium (air), and θ2 is the angle of refraction. 
Plugging in the values, we get: 
1.33sin37° = sinθ2 
θ2 ≈ 53° 
Therefore, the answer is choice B.

Question 19

The speed of light in material A is 1.4 times as large as it is in material B.What is the ratio of the refractive indices,nA/nB,of these materials?
A)1.4
B)1.2
C)1.0
D)0.80
E)0.71

Accepted Answer

The refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in a given medium. Thus, we have:
nA = c/vA
nB = c/vB
where c is the speed of light in vacuum, vA is the speed of light in material A, and vB is the speed of light in material B. From the given information, we have:
vA = 1.4vB
Substituting this into the expressions for the refractive indices, we get:
nA/nB = (c/vA)/(c/vB) = vB/vA = 1/1.4 = 0.71
Therefore, the ratio of the refractive indices is 0.71, which corresponds to choice (E).

Question 20

Blue light with a wavelength of 425 nm passes from a vacuum into a glass lens;and the index of refraction is found to be 1.65.The glass lens is replaced with a plastic lens.The index of refraction for the plastic lens is 1.54.In which one of the two lenses does the light have the greatest speed and what is that speed?
A)glass,2.28 × 10⁸ m/s
B)plastic,2.13 × 10⁸ m/s
C)glass,1.82 × 10⁸ m/s
D)plastic,1.95 × 10⁸ m/s
E)The speed of the blue light is the same in the vacuum and both lenses;and it is 2.99 × 10⁸ m/s.

Accepted Answer

The speed of light in a medium is given by $v = \frac{c}{n}$, where $c$ is the speed of light in vacuum (approximately $3.00 \times 10^8$ m/s) and $n$ is the index of refraction of the medium. The plastic lens has a lower index of refraction (1.54) compared to the glass lens (1.65), which means light travels faster in the plastic lens. The speed of light in the plastic lens is $v = \frac{3.00 \times 10^8 \, \text{m/s}}{1.54} \approx 1.95 \times 10^8 \, \text{m/s}$.

Quiz 26: The Refraction of Light: Lenses and Optical Instruments

What is the frequency of light that has a wavelength in water of 788 nm if the refractive index for this light is 1.33?

A fish swims 2.00 m below the surface of a pond.At what apparent depth does the fish appear to swim if viewed from directly above? The index of refraction of water is 1.33.

A beam of light passes from air into water.Which is necessarily true?

Light with a wavelength of 589 nm in a vacuum strikes the surface of an unknown liquid at an angle of 31.2° with respect to the normal to the surface.If the light travels at a speed of 1.97 × 10⁸ m/s through the liquid,what is the angle of refraction?

When certain light rays pass from a vacuum into a block of an unknown material,the measured index of refraction of the material is 3.00.What is the speed of light inside the block?

A grizzly bear is sitting on a rock in the middle of a calm river when she observes a fish directly below.If the apparent depth of the fish is 0.40 m,what is the actual depth at which the fish is swimming? The index of refraction of water is 1.33.

Complete the following statement: Fiber optics make use of

The bending of light as it moves from one medium to another with differing indices of refraction is due to a change in what property of the light?

A ray of light propagates in water (n = 1.333) and strikes a sheet of crown glass (n = 1.523) .If the angle of refraction in the glass is 35.2°,determine the angle of incidence.

Which one of the following expressions determines the critical angle for quartz (n = 1.5) immersed in oil (n = 1.1) ?

Which one of the following statements concerning the index of refraction for a given material is true?

A scuba diver shines a flashlight from beneath the surface of water (n = 1.33) such that the light strikes the water-air boundary with an angle of incidence of 37°.At what angle is the beam refracted?

The speed of light in material A is 1.4 times as large as it is in material B.What is the ratio of the refractive indices,nA/nB,of these materials?