Calculate the critical angle between diamond (n = 2.42) and quartz (n = 1.46)?

23°
37°
52°
60°

37°

Explanation:

Total internal reflection is a phenomenon that occurs when a ray of light is moving from a medium with higher index of refraction to a medium with lower index of refraction; in this case, there exist a value of the angle of incidence (called critical angle, ) above which no refraction occurs, and all the light is reflected back into the original medium.

The value of the critical angle between two mediums is given by the formula:

where

is the index of refraction of the 1st medium

is the index of refraction of the 2nd medium

In order to have total internal reflection, it must be .

In this problem:

is the index of refraction of diamond

is the index of refraction of quartz

Substituting, we find the value of the critical angle: