CBSE Class 12 · 2015 · Delhi · Wave OpticsShort Answer

Let $I_0$ be the intensity of the plane-polarized light after the first polaroid $P_1$, and let the middle sheet $P_3$ make an angle $\theta$ with $P_1$. By Malus' law the light emerging from $P_3$ is

Since $P_1$ and $P_2$ are crossed, the axis of $P_2$ makes $(90^{\circ }-\theta )$ with $P_3$. Applying Malus' law again at $P_2$:


This is maximum when $\sin 2\theta =1$, i.e. $2\theta =90^{\circ }\Rightarrow \theta =45^{\circ }$, giving $I_{max}=\frac{I_0}{4}$.