Worksheet: Refracted Light Ray Paths

In this worksheet, we will practice analyzing refraction that involves multiple boundaries, multiple rays, and boundaries at arbitrary angles to each other.

Q1:

A light ray traveling in air with a refractive index of 1.0 is refracted by the prism shown in the diagram, which is made of a substance with a refractive index of 1.6. What is the measure of the angle 𝜃 ?

Q2:

Two light rays travel through air and are incident on a layer of glass, as shown in the diagram. The rays pass through the layer of glass and arrive at the same point, from which they pass into a layer of plastic. Two rays emerge from the plastic layer. Does the ray that follows the path of incident ray I follow the path of emergent ray I or emergent ray II?

  • AEmergent ray II
  • BEmergent ray I

Q3:

Two rays that initially travel through air that has a refractive index of 1.0 are incident on different sides of a right-angled triangular prism made of a substance that has a refractive index of 1.45.

What is the angle between the emergent ray that follows the path of incident ray I and the normal to the surface from which it emerges?

What is the angle between the emergent ray that follows the path of incident ray II and the normal to the surface from which it emerges?

Q4:

A light ray passes from air into an object consisting of a region with a refractive index of 1.6 and a region with a refractive index of 1.4, following the path shown in the diagram. What is the ratio of the time that the light ray takes to pass through the 𝑛 = 1 . 6 region to the time that it takes to pass through the 𝑛 = 1 . 4 region?

Q5:

A light ray propagates through air that has a refractive index 𝑛 = 1 . 0 . The ray is incident on a plastic surface at an angle of 4 7 from the normal to the surface. The plastic has a refractive index 𝑛 = 1 . 3 5 and extends a distance 𝑦 perpendicular to the surface of 2.2 mm. Parallel to the plastic layer is a glass layer that has a refractive index 𝑛 = 1 . 5 and a length 𝑦 = 1 . 9 m m perpendicular to the surface. Find the distance Δ 𝑥 parallel to the surface of the plastic from the point at which the ray enters the plastic to the point at which the ray emerges from the glass.

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