State and explain Brewster's law of polarization.

Explanation

Statement of Brewster.s law
It states the tangent of polarising angle is equal to the refractive index of the material i.e.
`tan i_(p)=mu`
It is found that when light is incident in a transparent medium at polarising angle, the reflected and refracted rays are perpendicular to each other.
Malus found that an ordinary beam, on refracted from transparent medium, becomes partially polarised. The degree of polarisation increases as the angle of incidence is increased. At a particular angle of incidence, called as the polarising angle, the reflected beam becomes completely polarised.

AB is the incident ray and BC is the reflected ray at the polarising angle `i = i_(p)`. The reflected ray BC is plane polarised with its vibrations perpendicular to plane of the paper. A part of the light is refracted along BD. It is found that both the reflected ray and the refracted ray are perpendicular to each other i.e. `/_CBD=90^(@)`
`:. i_(p)+r=90^(@)`
or `r=90^(@)-i_(p)`
According to Snell.s law.
`mu=(sin i)/(sin r)=(sin i_(p))/(sin(90^(@)-i_(p))`
`=(sin i_(p))/(cos i_(p))=tan i_(p)`
Thus, the refractive index pf transparent medium is equal to tangent of polarising angle.
Given `i_(p)=60^(@)`
`:. mu-tan60^(@)=sqrt3`