Question

Two polaroids $P_1\text{and}{P}_2$ 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 $P_1\text{and}{P}_2$ such that its axis makes an angle ${45}^{\circ }$ with that of $P_1.$ The intensity of transmitted light through $P_2$ is

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

Answer 1

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

According to the question, the diagram is


From the above diagram, the intensity of transmitted light through $P_1$

$I_1=\frac{I_0}{2}$

The intensity of transmitted light through $P_3$,

$I_2=I_1{\cos }^2{45}^{\circ }=\frac{I_0}{2}{\cos }^2{45}^{\circ }$

$\Rightarrow I_2=\frac{I_0}{2}\times {\left(\frac{1}{\sqrt{2}}\right)}^2=\frac{I_0}{4}$

Angle between polaroids,

$P_3\text{and}{P}_2=90-45={45}^{\circ }$

$\therefore$ Intensity transmitted through $P_2,$

$I_3=I_2{\cos }^2{45}^{\circ }=\frac{I_0}{4}{\cos }^2{45}^{\circ }$

$\Rightarrow I_3=\frac{I_0}{4}\times {\left(\frac{1}{\sqrt{2}}\right)}^2=\frac{I_0}{8}$

Hence, $\left(C\right)$ is the correct answer.