Worksheet: Critical Angle for Total Internal Reflection
In this worksheet, we will practice relating the paths of refracted and internally reflected light rays to the refractive index of media they travel in.
Q1:
Which of the following formulas correctly shows the relation between the critical angle for total internal reflection for a light ray, the refractive index of the substance the light is propagating in, and the refractive index of the substance when the light is reflected from its surface?
- A
- B
- C
- D
- E
Q2:
What is the critical angle for a light ray traveling in water with a refractive index of 1.33 that is incident on the surface of water above which air is with a refractive index of 1.00? Answer to the nearest degree.
Q3:
What is the critical angle for a light ray traveling in water with a refractive index of 1.33 that is incident on the surface of water above which ice is with a refractive index of 1.31? Answer to the nearest degree.
Q4:
Light rays travel through kerosene. A layer of water that has a refractive index of 1.33 floats on the surface of the kerosene. Light rays that are incident on the interface of kerosene and water at angles of from the surface or less are totally internally reflected. What is the refractive index of the kerosene? Answer to three significant figures.
Q5:
The critical angle required for total internal reflection at a boundary between two substances is . The refractive index of the medium that light is reflected from is 1.1. What is the difference between the refractive index of the medium from which the light is reflected and the refractive index of the medium in which the light propagates before it is reflected?
Q6:
Light rays take the paths shown in the diagram between substances with refractive indexes , , and . Three paths are shown for the hypothetical raysβray I, ray II, and ray IIIβthat emerge from the substance with the refractive index into the substance with the refractive index .
Which of , , and is the largest refractive index?
- A
- B
- C
Which of , , and is the smallest refractive index?
- A
- B
- C
Which of ray I, ray II, and ray III correctly shows the path that light would take?
- ARay I
- BRay III
- CRay II
Q7:
The diagram shows a light ray that is transmitted from substance I to substance II at angle to the boundary between the substances. The ray is totally internally reflected back into substance II at the boundary to substance III. For any angle of greater than , the light ray is transmitted to substance II. Find the angle to the nearest degree.
Q8:
Light rays follow the paths shown in the diagram. Find the difference between the angles and . Answer to the nearest degree.
Q9:
A light ray propagates from one end of a fiber optic cable to the other end, as shown in the diagram. Midway between the ends of the cable, the ray is incident on the boundary between the core of the fiber and its cladding at an angle negligibly greater than the critical angle.
How many nanoseconds does it take for the ray to pass from one end of the fiber cable to the other?
If a cable like the cable shown were laid around the surface of Earth and a light ray propagated along it, reflecting as shown in the diagram, how many times per second would the light ray pass through the entire length of the cable? Use a value of 6,370 km for the radius of Earth. Answer to two decimal places.