Question

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

Answer 1

Answer:

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, $\theta_c$) 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:

$\theta_c = sin^{-1} (\frac{n_2}{n_1})$

where

$n_1$ is the index of refraction of the 1st medium

$n_2$ is the index of refraction of the 2nd medium

In order to have total internal reflection, it must be $n_1>n_2$.

In this problem:

$n_1=2.42$ is the index of refraction of diamond

$n_2=1.46$ is the index of refraction of quartz

Substituting, we find the value of the critical angle:

$\theta_c=sin^{-1}(\frac{1.46}{2.42})=37^{\circ}$