Question

(a) Why unpolarised light from a source do not show a variation in intensity when viewed through a polaroid which is rotated? Show with the help of a diagram, how unpolarised light from Sun gets linearly polarised by scattering.
(b) Three identical polaroid sheets $P_1,P_2$ and $P_3$ are oriented so that the pass axis of $P_2$ and $P_3$ are inclined at angles of ${60}^o$ and ${90}^o$ respectively with the pass axis of $P_1$. A monochromatic source S of unpolarised light of intensity $I_0$ is kept in front of the polaroid sheet $P_1$ as shown in the figure. Determine the intensities of light as observed by the observer at O, when polaroid $P_3$ is rotated with respect to $P_2$ at angles $\theta ={30}^o$ and ${60}^o$.

Answer 1

(a)

An unpolarized light wave has direction of vibration of electric field in all directions. When an unpolarized light is passed through a polaroid, output light wave is polarized in only one direction along the polaroid. As the polaroid is rotated, the intensity does not change as the original light wave has symmetric electric field in all directions. The attached figure shows the polarisation of sunlight by scattering from air molecules.

(b)

Output from polaroid 2 is given by:

$I_2=I_o{\cos }^2\left(60\right)$

$I_2=\frac{I_o}{4}$

When polaroid 3 is rotated by an angle of ${30}^o$ with respect to polaroid 2, final angle between polaroid 2 and polaroid 3 is equal to ${60}^o$. Then, intensity seen by O is:

$I_3=I_2{\cos }^2\left(60\right)$

$I_3=\frac{I_o}{16}$

When polaroid 3 is rotated by an angle of ${60}^o$ with respect to polaroid 2, final angle between polaroid 2 and polaroid 3 is equal to ${90}^o$. Then, intensity seen by O is:

$I_3=I_2{\cos }^2\left(90\right)$

$I_3=0$