When light of a certain wavelength is incident on a plane surface of a material at a glancing angle of  ${30}^{\circ }$, the reflected light is found to be completely plane polarized. Determine
angle of refraction in degrees 

a) Angle of incident light with the surface is  ${30}^{\circ }$. The angle of incidence $={90}^{\circ }-{30}^{\circ }={60}^{\circ }$. Since reflected light is completely polarized, therefore incidence takes place polarizing angle of incidence  ${\theta }_p$. 
 $\therefore {\theta }_p={60}^{\circ }$
Using Brewster’s law
 $\mu =\tan {\theta }_p=\tan {60}^{\circ }\mu =\sqrt{3}$
b) From Snell’s law 
 $\mu =\frac{\sin i}{\sin r\text{'}}\therefore \sqrt{3}=\frac{\sin {60}^{\circ }}{\sin r}$
Or  $\sin r=\frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{3}}=\frac{1}{2},r={30}^{\circ }$