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 work underwater 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 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 is defined as the angle of incidence at which the angle of refraction is 90 degrees. In other words, when the incident angle exceeds the critical angle, total internal reflection occurs and no light is transmitted through the interface.

Using Snell's law, we can write:

n1*sin(theta1) = n2*sin(theta2)

where n1 is the index of refraction of the medium the ray is coming from (air in this case), n2 is the index of refraction of the medium the ray is entering (the new solid), theta1 is the incident angle, and theta2 is the refracted angle.

At the critical angle, theta2 = 90 degrees, so sin(theta2) = 1. Plugging in the values from the problem:

1.00*sin(53 degrees) = n2*1

n2 = 1.06

Therefore, the index of refraction for the new solid is 1.06, which is choice C.

You Are Experimentally Determining the Critical Angle for a Novel