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Lesson Worksheet: Refracted Light Ray Paths Physics • 9th Grade

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 I
  • BEmergent ray II

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 47 from the normal to the surface. The plastic has a refractive index 𝑛=1.35 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=1.9mm perpendicular to the surface. Find the distance Δ𝑥 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.

Q6:

A light ray follows the path shown in the diagram through a prism, moving from air with a refractive index of 1.0 to glass with a refractive index of 1.5. Find 𝜃, knowing that the two unlabeled angles of the prism are equal to each other.

Q7:

Two light rays, ray I and ray II, travel antiparallel to each other, as shown in the diagram. The rays travel through air that has a refractive index of 1.0, and at an instant 𝑡, both of the rays are incident on opposite sides of a 2.5 cm long object consisting of two layers made from substances that have the refractive indices 𝑛=1.3 and 𝑛=1.5. At the instant that ray II emerges back into air, how far has ray I traveled in air since instant 𝑡?

Q8:

Two light rays, ray I and ray II, travel through air that has a refractive index of 1.0. The two rays are incident on the surface of a plastic layer that has a refractive index of 1.25 and whose thickness Δ𝑦 is 7.2 mm. Both rays emerge from the plastic layer at the same point. Ray II is incident at a distance of Δ𝑥=3.2mm to the right of the point where ray I is incident, both on the same surface. Ray I is incident at an angle of 𝜃=49 to the line normal to the surface of the plastic and ray II is incident at an angle of 𝜃 to the same line.

What is the incident angle 𝜃 of ray II?

What is the difference in angle Δ𝜃 between ray I and ray II when they emerge from the plastic layer?

What is the difference in angle Δ𝜃 between ray I and ray II when they travel through the plastic layer?

Q9:

A light ray traveling in air enters a plastic block at an angle of 76 to the normal to a surface of the block and exits the block at an angle 𝜃 to another surface of the block, as shown in the diagram. The block has a uniform refractive index. Find the value of 𝜃.

Q10:

A light ray traveling in air that has a refractive index of 1.0 is incident on the surface of glass that has a refractive index of 1.5, striking the surface at an angle 𝜃=65 from the normal to the surface. The ray passes through the glass and into a layer of plastic that has a refractive index of 1.3. The ray emerges from the plastic back into the air through a side of the plastic layer that is perpendicular to the side of the plastic layer at which the ray entered, as shown in the diagram. The angle between the path of the ray emerging from the plastic and the surface of the plastic from which the ray emerges is 𝜃. What is the ratio of 𝜃 to 𝜃?

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