Question

Two Polaroids are placed at 90° to each other and the transmitted intensity is zero. What happens when one of them is rotated ?

Answer 1

we know, In plane polarised light, electric field oscilates back and forth in a plane perpendicular to propagation of light.

the intensity of polarised through a polariser at an angle $\theta$ is given by, I = $I_0cos^2\theta$

but if two Polaroids e.g., N = 2 placed between the polariser and analyser with equal successive angular separation, then the overall intensity at the analyser is given by,
$I=I_0cos\left(\frac{\pi}{2N}\right)^{2N}$

so, $I=I_0cos\left(\frac{\pi}{4}\right)^4$

hence, $=\frac{I_0}{4}$

hence, when one them is rotated then, the intensity at the analyser will be one fourth of initial intensity of polariser.