Question

Unpolarized light of intensity 32 W m^-2 passes through three polarize 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. 30⁰
• B. 45⁰
• C. 22.5⁰
• D. 60⁰

Answer 1

Answer: (C)

22.5⁰

Answer 2

Let $\theta$ be angle between the axis of the first two polarizer’s then obviously $(90 - \theta)$ is the angle between 2^nd and 3^rd polariers.

$\therefore I = \frac{I_{0}}{2}\cos^{2}\theta\cos^{2}(90 - \theta)$

Or $2 = \frac{32}{2}\cos^{2}\theta\cos^{2}(90 - \theta) = 16\cos^{2}\theta\sin^{2}\theta$

$\frac{2}{16} = \cos^{2}\theta\sin^{2}\theta or(2\sin\theta\cos\theta)^{2} = \frac{1}{2}$

$\sin^{2}2\theta = \frac{1}{2}\therefore\sin 2\theta = \frac{1}{\sqrt{2}}$

$\therefore 2\theta = 45ºor\theta = 22.5º$