Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $\mathrm{P}_2$ and $P_3$ are inclined at an angle $60^{\circ}$ and $90^{\circ}$ with respect to axis of $\mathrm{P}_1$. The source has an intensity $I_0$. The intensity of transmitted light through $P_3$…

Question

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $\mathrm{P}_2$ and $P_3$ are inclined at an angle $60^{\circ}$ and $90^{\circ}$ with respect to axis of $\mathrm{P}_1$. The source has an intensity $I_0$. The intensity of transmitted light through $P_3$ is $\left(\cos 60^{\circ}=0.5, \cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$

Aicharya · Accepted Answer

According to Malus' law, $\mathrm{I}=\mathrm{I}_0 \cos ^2 \theta$
When beam passed through $\mathrm{P}_1$, $\mathrm{I}=\frac{\mathrm{I}_0}{2}$
When beam passed through $\mathrm{P}_2$, $\begin{aligned} \mathrm{I}_2 & =\frac{\mathrm{I}_0}{2} \cos ^2 60^{\circ} \\ \therefore \quad \mathrm{I}_2 & =\frac{\mathrm{I}_0}{8} \end{aligned}$
When beam passed through $\mathrm{P}_3$, $\mathrm{I}_3=\frac{\mathrm{I}_0}{8} \cos ^2 30^{\circ}=\frac{\mathrm{I}_0}{8} \times\left(\frac{\sqrt{3}}{2}\right)^2=\frac{3 \mathrm{I}_0}{32}$

Three identical polaroids $P_1, P_2$ and $P_3$ are placed one after another. The pass axis of $\mathrm{P}_2$…

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