Question

(a) Show, giving via suitable diagram, how unpolarized light can be polarised by reflection.
(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 ${60}^o$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Answer 1

(a)On reflection from a transparent medium a normal light beam becomes partially polarised. Higher the angle of incidence,higher the degree of polarisation.The reflected light beam becomes fully polarised at the polarising angle.Then

$\mu =tanp$

where $\mu$ is the refractive index of the refracting medium and $p$ is the polarising angle.

(b)Polaroids $P_1$ and $P_2$ have their axes perpendicular to each other and polaroid $P_3$ is at ${60}^0$ to $P_1$.

Intensity of light through $P_1$, $I^{\prime }=\frac{I_0}{2}$

Intensity of light through $P_3$, $I^{\prime \prime }=I^{\prime }co{s}^2\left({60}^0\right)=\frac{I_0}{2}co{s}^2\left({60}^0\right)=\frac{I_0}{8}$

Angle between $P_3$ and $P_2$ is ${30}^0$

Intensity of light through $P_2$,$I^{\prime \prime \prime }=I^{\prime \prime }co{s}^2\left({30}^0\right)=\frac{3I_0}{32}$