Question

(a) How does an unpolarized light incident on a Polaroid get polarized? Describe briefly, with the help of a necessary diagram, the polarization of light by reflection form a transparent medium.
(b) Two polaroids ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ are kept in crossed position. How should a third Polaroid ${}^{\prime }{C}^{\prime }$ be placed between them so that the intensity of polarized light transmitted by Polaroid $B$ reduces to $1/8$th of the intensity of unpolarized light incident of $A$?

Answer 1

(a)

When an unpolarized light is passed through a polaroid, then the light wave gets linearly polarized with the electric field vector oscillating along a direction perpendicular to the aligned molecules (pass-axis of polaroid).

The attached diagram shows polarisation by reflection from a transparent medium. When light is reflected, it becomes linearly polarized with electric field vector perpendicular to the plane of incidence.

(b)

After passing through polaroid A, intensity is given by:

$I_1=I/2$

Let polaroid C be placed at an angle $\theta$ to polaroid A. Then, by Malu's Law, output intensity from polaroid C is:

$I_2=\frac{I}{2}{\cos }^2\theta$

Angle between polaroid C and polaroid B is $\pi /2-\theta$.

$I_3=I_2{\cos }^2(\pi /2-\theta )=\frac{I}{2}{\cos }^2\theta {\sin }^2\theta$

$I_3=\frac{I}{8}{\sin }^2\left(2\theta \right)$

Given $I_3=\frac{I}{8}$

$\theta =\pi /4$