As shown in the figure, three identical polaroids $P_{1}, P_{2}$ and $P_{3}$ are placed one after an

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 $256 \frac{\mathrm{~W}}{\mathrm{~m}^{2}}$. The intensity of light at point $O$ is _______ $\frac{\mathrm{W}}{\mathrm{m}^{2}}$.\

Professor PC Thomas Classes · Answer

(24) : After $P_{1}, I_{1}=\frac{I_{0}}{2}$\ After $P_{2}$,\ $I_{2}=\frac{I_{0}}{2} \cos ^{2} 60^{\circ} \Rightarrow \frac{I_{0}}{2} 	imes\left(\frac{1}{4}ight)=\left(\frac{I_{0}}{8}ight)$\ After $P_{3}, I_{3}=I_{2} \cos ^{2} 30^{\circ}=\frac{I_{0}}{8} 	imes\left(\frac{\sqrt{3}}{2}ight)^{2}$\ $\left(\because 90^{\circ}-60^{\circ}=30^{\circ}ight)$\ $\Rightarrow I_{3}=\frac{3 I_{0}}{32} ; I_{3}=\frac{3 	imes 256}{32} \mathrm{~W} / \mathrm{m}^{2}$\ $\Rightarrow I_{3}=24 \mathrm{~W} / \mathrm{m}^{2}$\