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

Answer: 1.50

Intensity of polarised light
$I_P^{\prime }=I_P{\cos }^2\theta /2$
$\therefore I_{P^{\prime }}=\{\begin{array}{l}\max =I_P\\ \min =0\end{array}$
But intensity of unpolarised light remains const.
$\therefore I_0^{\prime }=I_0/2$
$\therefore I_{\max }=I_P+I_0/2$
$I_{\min }=I_0/2$
by problem $I_P+\frac{I_0}{2}=4\frac{I_0}{2}$
$\therefore \frac{I_P}{I_0}=\frac{3}{2}$