Question

Unpolarised light of intensity $32W{m}^{-2}$ passes through three polarizers such that transmission axis of first is crossed with third. If intensity of emerging light is $2W{m}^{-2}$, what is the angle of transmission axis between the first two polarisers?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${22.5}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${22.5}^{\circ }$

Let $\theta$ be angle between the axis of the first two polarisers then obviously $({90}^o-\theta )$ is the angle between $2^{nd}and{3}^{rd}$ polarisers.
$\therefore I=\frac{I_0}{2}co{s}^2\theta co{s}^2({90}^o-\theta )$

or $2=\frac{32}{2}co{s}^2\theta co{s}^2({90}^o-\theta )=16co{s}^2\theta si{n}^2\theta$

$(2sin\theta cos\theta {)}^2=\frac{1}{2}orsi{n}^{2}2\theta =\frac{1}{\sqrt{2}}$

$\therefore 2\theta ={45}^{o}or\theta ={22.5}^o$