Explain the polarisation of light by reflection,state Brewster's law,and derive its formula.

(N/A) When unpolarised light is incident on the surface of a transparent medium,the reflected light is partially plane-polarised,and the refracted light is also partially polarised. The state of polarisation of the reflected ray depends on the angle of incidence.
When a ray of light is incident on the surface of a transparent medium at a specific angle of incidence,the reflected ray is found to be totally plane-polarised. In this state,all the electric field vectors in the reflected ray are parallel to each other and perpendicular to the plane of incidence. This angle of incidence is called the polarising angle or Brewster's angle,denoted by $i_{B}$ or $\theta_{P}$.
At the polarising angle,the reflected ray and the refracted ray are perpendicular to each other. Therefore,the angle of refraction $r$ is given by $r = 90^{\circ} - i_{B}$.
According to Snell's law:
$\mu = \frac{\sin i_{B}}{\sin r}$
Substituting $r = 90^{\circ} - i_{B}$:
$\mu = \frac{\sin i_{B}}{\sin(90^{\circ} - i_{B})}$
$\mu = \frac{\sin i_{B}}{\cos i_{B}}$
$\mu = \tan i_{B}$
This is known as Brewster's law. It states that the tangent of the polarising angle of incidence is equal to the refractive index of the transparent medium.