# Worksheet: Total Internal Reflection

In this worksheet, we will practice calculating the critical angle for total internal reflection at the interface between two materials with different refractive indices.

Q1:

At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice? Use a value of 1.309 for the refractive index of ice and use a value of 1.333 for the refractive index of water.

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Q2:

Light rays, initially in air, are normally incident on the vertical surface of a glass prism, as shown in the accompanying diagram. The prism has a refractive index of 1.50. The slanted face of the prism is aligned at an angle above the horizontal.

What is the largest value for such that an incident ray is totally reflected at the slanted face?

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The prism is immersed in water. Find the largest value for such that the ray is totally reflected at the slanted face. Use a value of 1.333 for the refractive index of water.

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Q3:

The critical angle for light passing from diamond (refractive index of 2.42) to air (refractive index of 1.00) is . Zircon has a refractive index of 1.92. What is the critical angle for light passing from zircon to air?

Q4:

Water has a refractive index of 1.33. A substance has a critical angle of when submerged in water.

What is the refractive index of the substance?

Air has a refractive index of 1.00. What would be the critical angle for this substance in air?

Q5:

A light ray is propagating in water. Find the critical angle for the ray incident on an interface between air and water. Use a value of 1.33 for the refractive index of water.

Q6:

Find the critical angle for a light ray propagating in the core of an optical fiber. The ray is incident on the interface between the core and the cladding of the fiber. The core consists of plastic with a refractive index of 1.48 and the cladding consists of plastic with a refractive index of 1.44.

Q7:

You are using total internal reflection to make a corner reflector. The reflector is in air and the incident angle of light on the reflector is from its surface. What must the minimum index of refraction of the material from which the reflector is made be?

Q8:

A ray of light emitted beneath the surface of an unknown liquid with air above it undergoes total internal reflection as shown. What is the index of refraction of the liquid?