Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be…
Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_3$ is inserted in between $P_1$ and $\mathrm{P}_2$, at the particular angle between $\mathrm{P}_2$ and $\mathrm{P}_3$. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $\mathrm{P}_2$ and $\mathrm{P}_3$ is :
$\frac{\pi}{4}$
$\frac{\pi}{6}$
$\frac{\pi}{8}$
$\frac{\pi}{3}$
Solution
Through $P_2 I_1=I_0 \sin ^2\left(\frac{\pi}{2}-\theta\right)$ $I_1=I_0 \cos ^2 \theta$ Through $P_3 I_{\text {net }}=\left(I_0 \cos ^2 \theta\right) \sin ^2 \theta$ $I_{n c t}=\frac{I_0}{4}[\sin (2 \theta)]^2 \text { for max } I_{\text {net }} \theta=45^{\circ}$ So angle between $P_2$ and $P_3=\frac{\pi}{4}$ Correct Ans. (1)
