You are experimentally determining the critical angle for a novel transparent solid whose index of refraction is less than that of water (n=1.33) but greater than that of air (n=1.00). Your experimental method involves underwater work in which you observe whether there is any transmitted ray at the water/solid interface as you vary the angle of incidence on the solid surface. When your device reaches an incident angle of 53 degrees you find that the transmitted ray inside the solid vanishes. What is the index of refraction for this new solid?
A) 1.16
B) 0.57
C) 1.06
D) 0.53

Question

Quizplus · Accepted Answer

The critical angle can be calculated using the formula: 
θc = sin^-1(n2/n1)

where n1 is the index of refraction of the medium the incident ray is coming from (in this case water, n1=1.33) and n2 is the index of refraction of the medium the incident ray is entering (the novel solid).

At the critical angle, the angle of refraction is 90 degrees, so sin(90) = 1. Therefore, we can rearrange the formula to solve for n2:

n2 = n1 sin(θc)

From the given information, we know that θc = 53 degrees, so:

n2 = 1.33 sin(53)
n2 ≈ 1.06

Therefore, the index of refraction for the novel solid is approximately 1.06, which corresponds to choice C.

You Are Experimentally Determining the Critical Angle for a Novel