Question 1

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0.In this liquid,its frequency will be:

Accepted Answer

The frequency of light does not change when it enters a different medium; only its speed and wavelength change.

Question 2

A ray in glass is incident onto a water-glass interface,at an angle of incidence equal to half the critical angle for that interface.The indices of refraction for water and the glass are 1.33 and 1.43,respectively.The angle that the refracted ray in the water makes with the normal is closest to:

Accepted Answer

The critical angle θc for the water-glass interface is given by sin(θc) = n_water / n_glass = 1.33 / 1.43. The angle of incidence is half of this critical angle. Using Snell's law, n_glass * sin(θ_incidence) = n_water * sin(θ_refracted), we can solve for θ_refracted, which is closest to 37°.

Question 3

A glass plate whose index of refraction is 1.57 is immersed in a liquid.The surface of the glass is inclined at an angle of 54° with the vertical.A horizontal ray in the glass is incident on the interface.The liquid is an oil whose index of refraction is 1.40.The incident horizontal ray refracts at the interface.The angle that the refracted ray,in the oil,makes with the horizontal is closest to:

Accepted Answer

Snell's law: n1*sin(theta1) = n2*sin(theta2)n1 = 1.57, theta1 = 90 - 54 = 36 degrees, n2 = 1.40sin(theta2) = (n1/n2)*sin(theta1) = (1.57/1.40)*sin(36) = 0.198theta2 = 11.3 degrees

Question 4

A drop of unknown liquid is placed at the point on a glass surface where internal reflection is occurring at θ = 48°.The drop is heated until internal reflection occurs.What is the refractive index of the liquid if n_g= 1.60?

Accepted Answer

The critical angle for total internal reflection is given by θc = sin⁻¹(n₂/n₁), where n₂ is the refractive index of the liquid and n₁ is the refractive index of the glass. Given θc = 48° and n₁ = 1.60, we can solve for n₂: n₂ = n₁ * sin(θc) = 1.60 * sin(48°) ≈ 1.19.

Question 5

The speed of light in a material is 0.41 c.What is the critical angle of a light ray at the interface between the material and a vacuum?

Accepted Answer

The critical angle can be calculated using Snell's Law. The refractive index of the material is the ratio of the speed of light in vacuum to the speed of light in the material, which is 1/0.41. Using the formula for the critical angle, sin(critical angle) = 1/refractive index, we find the critical angle to be approximately 24°.

Question 6

A ray in glass arrives at the glass-water interface at an angle of 48° with the normal.The refracted ray,in water,makes a 62° angle with the normal.The index of refraction of water is 1.33.In the figure,the angle of incidence of a different ray in the glass is 25°.The angle of refraction in the water is closest to:

Accepted Answer

The answer of  A ray in glass arrives at...

Question 7

A light ray (red)enters a concentrically cladded optical fiber at its center and an angle of 29.0° to the axis of the fiber.The diameter of the fiber is 1.0 mm and its refractive index is nf = 1.35.What must be the value of ncladding to guarantee total internal reflection? (n_air = 1.00)

Accepted Answer

To ensure total internal reflection, the refractive index of the cladding (n_cladding) must be less than the refractive index of the core (n_fiber = 1.35). The critical angle for total internal reflection is given by sin(θ_c) = n_cladding / n_fiber. For the light to be totally internally reflected, the angle of incidence inside the fiber must be greater than the critical angle. Given the angle of incidence is 29.0°, we need n_cladding < n_fiber * sin(29.0°). Calculating this gives n_cladding < 1.35 * sin(29.0°) ≈ 1.18. Thus, the correct choice is A) 1.18.

Question 8

A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed.How deep does the stream appear to the fisherman? Assume that the index of refraction of the water is 1.33.

Accepted Answer

The apparent depth can be calculated using the formula: apparent depth = real depth / refractive index. Here, apparent depth = 39 cm / 1.33 = 29 cm.

Question 9

The index of refraction of the core of a piece of fiber optic cable is 1.72.If the index of the surrounding cladding is 1.41,what is the critical angle for total internal reflection for a light ray in the core incident on the core-cladding interface?

Accepted Answer

The critical angle for total internal reflection is given by the equation:sin(critical angle) = n2/n1where n1 is the index of refraction of the less dense medium (in this case, the cladding) and n2 is the index of refraction of the more dense medium (in this case, the core).Plugging in the given values, we get:sin(critical angle) = 1.41/1.72critical angle = sin^-1(1.41/1.72)critical angle = 55.1°

Question 10

A ray in glass arrives at the glass-water interface at an angle of 48° with the normal.The refracted ray,in water,makes a 68° angle with the normal.The index of refraction of water is 1.33.In the figure,the angle of incidence of a different ray in the glass is 29°.The angle of refraction in the water is closest to:

Accepted Answer

The answer of  A ray in glass arrives at...

Question 11

A tank holds a layer of oil,1.70 m thick,which floats on a layer of syrup that is 0.74 m thick.Both liquids are clear and do not intermix.A ray,which originates at the bottom of the tank on a vertical axis,crosses the oil-syrup interface at a point 0.90 m from the axis.The ray continues and arrives at the oil-air interface,2.00 m from the axis and at the critical angle.In the figure,the index of refraction of the oil is closest to:

Accepted Answer

The answer of  A tank holds a layer of...

Question 12

Light having a speed in vacuum of 3.0 × 10⁸ m/s enters a liquid of refractive index 2.0.In this liquid,its speed will be:

Accepted Answer

The speed of light in a material is given by v = c/n, where c is the speed of light in vacuum and n is the refractive index of the material. Substituting c = 3.0 × 10^8 m/s and n = 2.0, we get v = 1.5 × 10^8 m/s. Therefore, the correct choice is C), which corresponds to 1.5 × 10^8 m/s.

Question 13

Two plane mirrors make an angle of 30°.A light ray enters the system and is reflected once off each mirror.Through what angle is the ray turned?

Accepted Answer

The ray is reflected at 30° from the first mirror and then at 30° from the second mirror. The total angle turned is 30° + 30° = 60°.

Question 14

A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (n_water = 1.33)

Accepted Answer

The answer of A fish appears to be 2.00 m...

Question 15

A ray in air is incident on a glass plate whose index of refraction is 1.42.The angle of refraction is one-half the angle of reflection.The angle of refraction is closest to:

Accepted Answer

The angle of refraction is one-half the angle of reflection, so the angle of refraction is 45°/2 = 22.5°. The closest choice to 22.5° is 43°.

Question 16

The critical angle for an air-glass interface is 10.9 degrees.A ray in air is incident on the interface.The reflected ray is 100 percent polarized.The angle of refraction is closest to:

Accepted Answer

The answer of The critical angle for an air-glass interface...

Question 17

A glass plate whose index of refraction is 1.66 is immersed in a liquid.The surface of the glass is inclined at an angle of 44° with the vertical.A horizontal ray in the glass is incident on the interface.When the liquid is a certain alcohol,the incident ray arrives at the interface at the critical angle.The index of refraction of the alcohol is closest to:

Accepted Answer

The critical angle is the angle of incidence at which the refracted ray is parallel to the interface. For a glass-liquid interface, the critical angle is given by:sin(critical angle) = n2/n1where n1 is the index of refraction of the glass and n2 is the index of refraction of the liquid.In this case, n1 = 1.66 and the critical angle is 44°. Therefore, sin(44°) = n2/1.66, which gives n2 = 1.15.

Question 18

A tank holds a layer of oil,1.58 m thick,which floats on a layer of syrup that is 0.66 m thick.Both liquids are clear and do not intermix.A ray,which originates at the bottom of the tank on a vertical axis,crosses the oil-syrup interface at a point 0.90 m from the axis.The ray continues and arrives at the oil-air interface,2.00 m from the axis and at the critical angle.In the figure,the index of refraction of the syrup is closest to:

Accepted Answer

The answer of  A tank holds a layer of...

Question 19

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0.In this liquid,its wavelength will be:

Accepted Answer

The relationship between the wavelength of light in vacuum and the wavelength of light in a medium is given by:
λ_medium=λ_vacuum/n
where λ_medium is the wavelength of light in the medium, λ_vacuum is the wavelength of light in vacuum and n is the refractive index of the medium.
Substituting the given values, we get:
λ_medium=λ_vacuum/2.0
λ_medium=600 nm/2.0
λ_medium=300 nm
Therefore, the wavelength of light in the given liquid is 300 nm.

Question 20

A cylindrical tank is 50.0 ft deep,37.5 ft in diameter,and filled to the top with water.A flashlight shines into the tank from above.What minimum angle φ can its beam make with the water surface if the beam is to illuminate part of the bottom? (nwater = 1.33)

Accepted Answer

The critical angle for total internal reflection at the water-air interface is given by θc = arcsin(1/nwater) = arcsin(1/1.33) ≈ 48.75°. For the light to reach the bottom, it must refract into the water, so φ must be less than the critical angle. Using Snell's Law and geometry, the minimum angle φ is calculated to be approximately 37.1°.

Quiz 18: Ray Optics

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0.In this liquid,its frequency will be:

A ray in glass is incident onto a water-glass interface,at an angle of incidence equal to half the critical angle for that interface.The indices of refraction for water and the glass are 1.33 and 1.43,respectively.The angle that the refracted ray in the water makes with the normal is closest to:

A drop of unknown liquid is placed at the point on a glass surface where internal reflection is occurring at θ = 48°.The drop is heated until internal reflection occurs.What is the refractive index of the liquid if n_g= 1.60?

The speed of light in a material is 0.41 c.What is the critical angle of a light ray at the interface between the material and a vacuum?

A light ray (red) enters a concentrically cladded optical fiber at its center and an angle of 29.0° to the axis of the fiber.The diameter of the fiber is 1.0 mm and its refractive index is nf = 1.35.What must be the value of ncladding to guarantee total internal reflection? (n_air = 1.00)

A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed.How deep does the stream appear to the fisherman? Assume that the index of refraction of the water is 1.33.

The index of refraction of the core of a piece of fiber optic cable is 1.72.If the index of the surrounding cladding is 1.41,what is the critical angle for total internal reflection for a light ray in the core incident on the core-cladding interface?

Light having a speed in vacuum of 3.0 × 10⁸ m/s enters a liquid of refractive index 2.0.In this liquid,its speed will be:

Two plane mirrors make an angle of 30°.A light ray enters the system and is reflected once off each mirror.Through what angle is the ray turned?

A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (n_water = 1.33)

A ray in air is incident on a glass plate whose index of refraction is 1.42.The angle of refraction is one-half the angle of reflection.The angle of refraction is closest to:

The critical angle for an air-glass interface is 10.9 degrees.A ray in air is incident on the interface.The reflected ray is 100 percent polarized.The angle of refraction is closest to:

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0.In this liquid,its wavelength will be:

A cylindrical tank is 50.0 ft deep,37.5 ft in diameter,and filled to the top with water.A flashlight shines into the tank from above.What minimum angle φ can its beam make with the water surface if the beam is to illuminate part of the bottom? (nwater = 1.33)

Quiz 18: Ray Optics

Light having a frequency in vacuum of 6.0 × 1014 Hz enters a liquid of refractive index 2.0.In this liquid,its frequency will be:

A ray in glass is incident onto a water-glass interface,at an angle of incidence equal to half the critical angle for that interface.The indices of refraction for water and the glass are 1.33 and 1.43,respectively.The angle that the refracted ray in the water makes with the normal is closest to:

A drop of unknown liquid is placed at the point on a glass surface where internal reflection is occurring at θ = 48°.The drop is heated until internal reflection occurs.What is the refractive index of the liquid if ng = 1.60?

The speed of light in a material is 0.41 c.What is the critical angle of a light ray at the interface between the material and a vacuum?

A light ray (red) enters a concentrically cladded optical fiber at its center and an angle of 29.0° to the axis of the fiber.The diameter of the fiber is 1.0 mm and its refractive index is nf = 1.35.What must be the value of ncladding to guarantee total internal reflection? (nair = 1.00)

A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed.How deep does the stream appear to the fisherman? Assume that the index of refraction of the water is 1.33.

The index of refraction of the core of a piece of fiber optic cable is 1.72.If the index of the surrounding cladding is 1.41,what is the critical angle for total internal reflection for a light ray in the core incident on the core-cladding interface?

Light having a speed in vacuum of 3.0 × 108 m/s enters a liquid of refractive index 2.0.In this liquid,its speed will be:

Two plane mirrors make an angle of 30°.A light ray enters the system and is reflected once off each mirror.Through what angle is the ray turned?

A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (nwater = 1.33)

A ray in air is incident on a glass plate whose index of refraction is 1.42.The angle of refraction is one-half the angle of reflection.The angle of refraction is closest to:

The critical angle for an air-glass interface is 10.9 degrees.A ray in air is incident on the interface.The reflected ray is 100 percent polarized.The angle of refraction is closest to:

Light having a wavelength in vacuum of 600 nm enters a liquid of refractive index 2.0.In this liquid,its wavelength will be:

A cylindrical tank is 50.0 ft deep,37.5 ft in diameter,and filled to the top with water.A flashlight shines into the tank from above.What minimum angle φ can its beam make with the water surface if the beam is to illuminate part of the bottom? (nwater = 1.33)

Light having a frequency in vacuum of 6.0 × 10¹⁴ Hz enters a liquid of refractive index 2.0.In this liquid,its frequency will be:

A drop of unknown liquid is placed at the point on a glass surface where internal reflection is occurring at θ = 48°.The drop is heated until internal reflection occurs.What is the refractive index of the liquid if n_g= 1.60?

A light ray (red) enters a concentrically cladded optical fiber at its center and an angle of 29.0° to the axis of the fiber.The diameter of the fiber is 1.0 mm and its refractive index is nf = 1.35.What must be the value of ncladding to guarantee total internal reflection? (n_air = 1.00)

Light having a speed in vacuum of 3.0 × 10⁸ m/s enters a liquid of refractive index 2.0.In this liquid,its speed will be:

A fish appears to be 2.00 m below the surface of a pond when viewed almost directly above by a fisherman.What is the actual depth of the fish? (n_water = 1.33)