Q.State Brewster's law. Derive the relation $n=\tan\theta_B$ between the refractive index of a medium and its polarizing angle $\theta_B$, starting from the fact that the reflected and refracted rays are perpendicular to each other at this angle.

Brewster's law states that when unpolarized light is incident on the boundary of a transparent medium at one particular angle, the polarizing angle $\theta_B$, the reflected ray is completely (100 percent) plane polarized, with vibrations perpendicular to the plane of incidence, while the refracted ray remains only partially polarized. This special condition occurs precisely when the reflected ray and the refracted ray are mutually perpendicular to each other.

If the angle of incidence is $\theta_B$ and the angle of reflection therefore also equals $\theta_B$ (law of reflection), and the reflected and refracted rays are perpendicular, then since the reflected ray, the refracted ray and the normal all meet at the point of incidence, the angle of refraction $\theta_r$ must satisfy

Applying Snell's law for light going from air (refractive index 1) into the medium (refractive index $n$), …

Use the perpendicularity of the reflected and refracted rays to write $\theta_r=90^\circ-\theta_B$, then substitute into Snell's law a …

• Forgetting WHY $\theta_r=90^\circ-\theta_B$ -- it follows from the stated perpendicularity of the reflected and refracted rays, not from any general geometric fact. …