Discuss the intensity of transmitted light when a Polaroid sheet is rotated between two crossed polaroids.

Let I₀ be the intensity of polarized light after passing through the first polarizer P₁. Then the intensity of light after passing through $\mathrm{I}={\mathrm{I}}_0{\cos }^2\mathrm{\theta }$

${\mathrm{I}}^1=\frac{\mathrm{I}}{2}{\cos }^2{\mathrm{\theta }}_1\cdot {\mathrm{Cos}}^2{\mathrm{\theta }}_2$
Where $\mathrm{\theta }$ is the angle between pass axes of P₁ and P₂, since, P₁ and P₃ are crossed the angle between the pass axes of P₂ and P₃ will be $(\mathrm{\pi }/2-\mathrm{\theta })$. Hence the intensity of light emerging from P₃ will be
$\begin{array}{l}\mathrm{I}={\mathrm{I}}_0{\cos }^2{\mathrm{\theta cos}}^2\left(\frac{\mathrm{\pi }}{2}-\mathrm{\theta }\right)\\ {\mathrm{I}}_0{\cos }^2{\mathrm{\theta sin}}^2\mathrm{\theta }=\frac{{\mathrm{I}}_0}{4}{\sin }^{2}2\mathrm{\theta }\end{array}$
Therefore, the transmitted intensity will be maximum when $\mathrm{\theta }=\frac{\mathrm{\pi }}{4}$