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 $45^{\circ}$ with that of $P_{1}$. Then intensity of transmitted light through $P_{2}$ is $\frac{I_{0}}{n}$. Find $n$.

Answer 1

$I_{1}=\frac{I_{0}}{2}$
$I_{2}=\frac{I_{0}}{2} \cos ^{2} 45^{\circ}=\frac{I_{0}}{4}$
$I_{3}=\frac{I_{0}}{4} \cos ^{2} 45^{\circ}=\frac{I_{0}}{8}$