Two polaroids $P_1$ and $P_2$ are set in crossed positions. A third polaroid $P_3$ is placed between the two making an angle $α$ with the axis passing from the first polaroid $P_1$. In what orientation will the transmitted intensity be maximum?

$\frac{π}{4}$

The correct answer is Option (3) → $\frac{π}{4}$

According to Maul's law,

$I=I_0\cos^2θ$

After $P_1$,

$I_1=\frac{I_0}{2}$

After $P_2$,

$I_2=I_1\cos^2α$

After $P_3$,

$I_3=I_2\cos^2(90-α)$

$=\frac{I_0}{2}\cos^2α\sin^2α$

and,

$\frac{I_0}{2}\cos^2α\sin^2α=\frac{1}{4}\sin^2(2α)$

$⇒2α=90°⇒α=45°$