Question

As shown in the figure, three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angle of $60^{\circ}$ and $90^{\circ}$ with respect to axis of $P_1$. The source $S$ has an intensity of $256 \frac{ W }{ m ^2}$. The intensity of light at point $O$ is ____ $\frac{W}{m^2}$

Answer 1

By first polaroid $P_1$ intensity will be halved then $P_2$ and $P_3$ will make intensity $\cos ^2\left(60^{\circ}\right)$ and $\cos ^2\left(30^{\circ}\right)$ times respectively.
Intensity out $=\frac{256}{2} \times \frac{1}{4} \times\left(\frac{\sqrt{3}}{2}\right)^2=\frac{256 \times 3}{2 \times 4 \times 4}= 2 4$