Question

(a) Show, with the help of a diagram, how unpolarised sunlight gets polarised due to scattering.
(b) 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 ${45}^o$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Answer 1

(a)

Unpolarized light scattering from air molecules shakes their electrons perpendicular to the direction of the original ray. The scattered light therefore has a polarization perpendicular to the original direction and none parallel to the original direction.
(b)

Intensity of light is halved after passing through a polaroid.

Hence, intensity of light transmitted through $P_1$ is $I_{P1}=\frac{I_o}{2}$

Axis of $P_3$ makes an angle of ${45}^o$ with the axis of $P_1$. Also, axis of $P_1$ and $P_2$ are perpendicular to each other. Hence, angle between axis of $P_2$ and $P_3$ is ${45}^o$.

After passing through $P_3$,

$I_{P3}=I_{P1}{\cos }^2\left(\pi /4\right)=\frac{I_o}{4}$

After passing through $P_2$,

$I_{P2}=I_{P3}{\cos }^2\left(\pi /4\right)=\frac{I_o}{8}$