Question

Two polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third Polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its pass axis makes an angle of 30${}^o$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Answer 1

Intensity of light passing through a single polaroid is halved when unpolarized light is incident on it.

Hence, $I_1=\frac{I_o}{2}$

Now, angle between $P_1$ and $P_2$ is ${30}^o$.

By Malus' Law,

$I_2=I_{1}co{s}^2\left(\varphi \right)$

$=I_{1}co{s}^2\left({30}^o\right)$

$=\frac{3I_o}{8}$

Angle between $P_2$ and $P_3$ is ${60}^o$.

By Malus' Law,

$I_3=I_{2}co{s}^2\left(\varphi \right)$

$=I_{2}co{s}^2\left({60}^o\right)$

$=\frac{3I_o}{16}$