Question

A mixture of plane polarised and unpolarised light falls normally on a polarising sheet. On rotating the polarizing sheet about the direction of the incident beam, the transmitted intensity varies by a factor of $4$. Find the ratio of the intensities $I_{P}$ and $I_{0}$, respectively, of the polarised and unpolarised components in the incident beam.

Answer 1

Intensity of polarised light
$I _{ P }'= I _{ P } \cos ^{2} \theta / 2$
$\therefore I_{P'}=\begin{cases}\max =I_{P} \\ \min =0\end{cases}$
But intensity of unpolarised light remains const.
$\therefore I _{0}'= I_{0} / 2$
$\therefore I _{\max } = I _{ P }+ I _{0} / 2$
$I _{\min } = I _{0} / 2$
by problem $I_{P}+\frac{I_{0}}{2}=4 \frac{I_{0}}{2}$
$\therefore \frac{ I _{ P }}{ I _{0}}=\frac{3}{2}$