Question

Unpolarized light of intensity $32W{m}^{-2}$ passes through three polarizers arranged such that the transmission axes of the first and the last polarizer are at right angles. If the intensity of emerging light is $3W{m}^{-2}$ , then what is the angle (in degree) between the transmission axes of the first two polarizers?

Answer 1

Answer: 30

Since unpolarized light is passing through the first polarizer, hence the intensity of light after crossing the first polarizer will be
$I_1=\frac{1}{2}{I}_0=16W{m}^{-2}$
Let us assume that the angle between the transmission axis of the first and second polarizer is $\theta$ , then from Malus law we can find out the intensity of light after it crosses the second polarizer.
$I_2=I_{1}co{s}^2\theta =16co{s}^2\theta$
Similarly, the intensity of light after crossing the third polarizer is
$I_3=I_2{\left(cos\right)}^2\left(90^{\circ }-\theta \right)=16{\left(cos\right)}^2\theta {\left(sin\right)}^2\theta$
$\Rightarrow I_3=16co{s}^2\theta si{n}^2\theta =3$
$\Rightarrow 4co{s}^2\theta si{n}^2\theta =\frac{3}{4}$
$\Rightarrow {\left(sin\right)}^2\left(2\theta \right)=\frac{3}{4}$
$\theta =30^{\circ }$