Question

Two polaroids are oriented with their planes perpendicular to incident light and transmission axis making an angle of ${30}^{\circ }$ with each other. What fraction of incident unpolarised light is transmitted ?

• A. $20\%$
• B. $45\%$
• C. $37.5\%$
• D. $75\%$

Answer 1

The correct option is C $37.5\%$

If unpolarised light is passed through a polariod $P_1$, its intensity will become half.
So $I_1=\frac{1}{2}{I}_0$ with vibrations parallel to the axis of $P_1$.
Now this light will pass through second polaroid $P_2$ whose axis is inclined at an angle of ${30}^{\circ }$ to the axis of $P_1$ and hence, vibrations of $I_1$. So in accordance with Malus law, the intensity of light emerging from $P_2$ will be
$I_2=I_1{\cos }^2{30}^{\circ }=\left(\frac{1}{2}{I}_0\right){\left(\frac{\sqrt{3}}{2}\right)}^2=\frac{3}{8}{I}_0$
$\frac{I_2}{I_0}=\frac{3}{8}=37.5\%$