Brewster's Law and Uses of Polaroid

Ordinary reflection also produces partial polarization, and at one particular angle of incidence, called the polarizing angle (or Brewster's angle) $\theta_B$, the reflected ray becomes completely (100 percent) plane polarized, with its vibrations entirely perpendicular to the plane of incidence, while the (weaker) refracted ray remains only partially polarized. Brewster found, and it can be shown from Snell's law, that this special condition occurs exactly when the reflected and refracted rays are mutually perpendicular to each other, i.e. $\theta_B+\theta_r=90^\circ$, so that $\theta_r=90^\circ-\theta_B$.

Substituting this into Snell's law $n=\sin\theta_B/\sin\theta_r$ for light going from air (or vacuum) into a medium of refractive index $n$ gives $n=\sin\theta_B/\sin(90^\circ-\theta_B)=\sin\theta_B/\cos\theta_B$, i.e.

which is Brewster's law: the refractive index of a medium equals the tangent of its polarizing angle. For ordinary glass ($n\approx1.5$), for instance, this gives a polarizing angle close to $56.3^\circ$. …