Q.The polarizing angle for light incident on a certain transparent medium from air is found to be $53^\circ$. Calculate the refractive index of the medium, and state the angle the refracted ray makes with the normal at this angle of incidence.

Given: polarizing angle $\theta_B=53^\circ$.

By Brewster's law, $n=\tan\theta_B=\tan53^\circ\approx1.327$.

Since the reflected and refracted rays are mutually perpendicular at the polarizing angle, $\theta_B+\theta_r=90^\circ$, so …

Apply $n=\tan\theta_B$ directly, then use $\theta_r=90^\circ-\theta …

• Computing $n=\sin\theta_B$ or $n=\cos\theta_B$ instead of $n=\tan\theta_B$. …