Q.What is Brewster's law? Derive the formula for Brewster's angle.

At Brewster's angle the reflected and refracted rays are perpendicular, which forces $\tan\theta_B = n$.

Brewster's law states that when unpolarised light is incident on a transparent medium at a particular angle, called the polarising angle or Brewster's angle $\theta_B$, the reflected light is completely plane-polarised, and the tangent of this angle equals the refractive index of the medium:

$\tan\theta_B = n$

Derivation: At Brewster's angle, the reflected ray and the refracted ray are found (experimentally, and consistent with the polarised-dipole-radiation picture) to be mutually perpendicular:

$\theta_B + \theta_r = 90^\circ \;\Rightarrow\; \theta_r = 90^\circ - \theta_B$

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