Question

Calculate the ratio of the critical angle of diamond to the critical angle of crown glass if both are surrounded by a vacuum.

Answer 1

The critical angle for a material is

$$\theta=\sin^{-1}\frac 1n.$$

Therefore, for the diamond and crown glass, we have

$$\frac{\theta_d}{\theta_g}=\frac{\arcsin(1/n_d)}{\arcsin(1/n_g)}=\frac{\arcsin(1/2.417)}{\arcsin(1/1.517)}=0.59.$$