Explain polarisation of light by reflection and write the Brewster's law and get the formula.

Explanation

A scientist named Malus discovered that the reflected ray is partically plane polarised when light rays incident on the surface of the transparent medium and the refracted ray is also partially polarised.
State of polarization of reflected ray depends on angle of incidence.

When a ray of light is incident on a surface of transparent medium at some definite angle of incidence, reflected ray is found to be totally plane polarized. In this state all the light vectors in the reflected ray of light are parallel to each other and perpendicular to the plane of incidence. This is called `sigma` components and since it contains 15% component of incidence ray, hence the reflected ray is fade.
In refracted rays there are 85% `sigma` components of incident ray and are all tt components and hence it slightly fade compare to incident ray.
When a ray of light is incident on a surface of transparent medium at some define angle of incidence, reflected ray is found to be totally plane polarised. Such an angle of incidence is called angle of polarisation of the given transparent medium. This angle is denoted by `i_(B)` or `theta_(P)`.
From Smells. law at a given point,
`mu=(sini_(B))/(sinr)" but "r=(pi)/(2)-i_(B)`
`:.mu=(sini_(B))/(sin((pi)/(2)-i_(B)))=(sini_(B))/(cosi_(B))`
`:.mu=tani_(B)`
This is called Brewster.s law. In words, when a ray reflected from a surface of transparent object is totally plane polarized the tangent of the angle of incidence is equal to the refractive index of the material of the object.