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.

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

${i}_{p}+{90}^{\xb0}+r={180}^{\xb0}\phantom{\rule{0ex}{0ex}}\Rightarrow r={90}^{\xb0}-{i}_{p}$

Then according to Snell's law

$\mu =\frac{\mathrm{sin}{i}_{p}}{\mathrm{sin}r}\phantom{\rule{0ex}{0ex}}\Rightarrow \mu =\frac{\mathrm{sin}{i}_{p}}{\mathrm{sin}\left({90}^{\xb0}-{i}_{p}\right)}\phantom{\rule{0ex}{0ex}}\Rightarrow \mu =\frac{\mathrm{sin}{i}_{p}}{\mathrm{cos}{i}_{p}}\phantom{\rule{0ex}{0ex}}\Rightarrow \mu =\mathrm{tan}{i}_{p}$

where $\mu $ is the refracted index of the transparent medium. This is called Brewster's law and i

_{p}is called the Brewster angle.

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