Question

A light ray is incident upon a plane interface between two materials. The ray makes an incident angle with the normal to the surface of 30 degrees in a material with an index of retion of 1.3. If the second material has an index of retion of 1.8, what is the reted angle (in degrees) in that material?

A. 24.55 ∘
B. 37.12 ∘
C. 52.88 ∘
D. 65.45 ∘

Answer 1

The refracted angle in the second material is approximately 21.8 degrees when a light ray with an incident angle of 30 degrees crosses from a material with an index of refraction of 1.3 to a material with an index of refraction of 1.8.

Step-by-step explanation:

When a light ray crosses from one material to another, it is refracted, or bent, at the boundary between the two materials. The amount of bending depends on the indices of refraction of the two materials. The index of refraction is a measure of how much the material slows down light compared to its speed in a vacuum. In this case, the incident angle is 30 degrees in a material with an index of refraction of 1.3, and the second material has an index of refraction of 1.8. We can use Snell's law to calculate the refracted angle:

n1sin(θ1) = n2sin(θ2)

where n1 and n2 are the indices of refraction and θ1 and θ2 are the incident and refracted angles, respectively.

Substituting the given values, we have:

n1sin(30°) = 1.3sin(θ2)

1.3(0.5) = 1.8sin(θ2)

0.65 = 1.8sin(θ2)

sin(θ2) ≈ 0.36

θ2 ≈ sin-1(0.36) ≈ 21.8°

Therefore, the refracted angle in the second material is approximately 21.8 degrees.