Question

In figure suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed $\omega$. That if unpolarized light is incident on the left disk with an intensity $I_{\max }$ the intensity of the beam emerging from the right disk is given by $I=\frac{1}{x} I_{\max }(1-\cos y \omega t)$. Find $(x y)$.

Answer 1

By Malus law
$I=I_{0} \cos ^{2} \theta \quad \theta$ is the angle between two axis of polaroid.

Third polaroids maches $\left(90^{\circ}-\theta\right)$ with II ${ }^{\text {nd }}$ polaroids.
$I=\frac{I_{\max }}{2} \cos ^{2} \theta \cdot \cos ^{2}\left(90^{\circ}-\theta\right)$
$\Rightarrow I=\frac{I_{\max }}{2} \cos ^{2} \theta \cdot \sin ^{2} \theta \times \frac{4}{4}$
$\Rightarrow I=\frac{I_{\max }}{8} \sin ^{2} 2 \theta$
$\Rightarrow I=\frac{I_{\max }}{8}\left(\frac{1-\cos 4 \omega t}{2}\right)$
$\Rightarrow I=\frac{I_{\max }}{16}(1-4 \cos \omega t)$