An unpolarised light is incident on the boundary between two transport media.State the condition when the reflected wave is totally plane polarised. Find out the expression for the angle of incidence in this case.

Dear student

In unpolarized light the light vibrate in all possible planes but for polarised light the vibrations occur in a single plane.
The reflected wave will be totally polarised if reflected wave and refracted wave are perpendicular to each other.

If the incident angle is i_p and refracted angle r then 
$$\begin{gathered} i_p+{90}^{°}+r={180}^{°} \\ \Rightarrow r={90}^{°}-i_p \end{gathered}$$
Then according to Snell's law 
$$\begin{gathered} \mu =\frac{\sin i_p}{\sin r} \\ \Rightarrow \mu =\frac{\sin i_p}{\sin \left({90}^{°}-i_p\right)} \\ \Rightarrow \mu =\frac{\sin i_p}{\cos i_p} \\ \Rightarrow \mu =\tan i_p \end{gathered}$$
where $\mu$ is the refracted index of the transparent medium. This is called Brewster's law and i_p is called the Brewster angle.