Question

Two Polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle ${45}^o$ with that of $P_1$. The intensity of transmitted light through $P_2$ is:

• A. $\frac{I_0}{16}$
• B. $\frac{I_0}{2}$
• C. $\frac{I_0}{4}$
• D. $\frac{I_0}{8}$

Answer 1

The correct option is D $\frac{I_0}{8}$

Initial intensity $=I_0$
After $P_1\to I_1=\frac{I_0}{2}$
After $P_3\to I_2=I_{1}co{s}^2{45}^o$
$=\frac{I_0}{2}\times \frac{1}{2}$
$=\frac{I_0}{4}$
After $P_2\to I_3=I_{2}co{s}^2{45}^o$
$=\frac{I_0}{4}\times \frac{a}{2}=\frac{I_0}{8}$