Question

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets, if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam?

• A. ${75}^{\circ }$
• B. ${55}^{\circ }$
• C. ${35}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is B ${55}^{\circ }$

$I_2,I_1$ are the intensity of final and first transmitted beam and $\theta$ is the angle between the characteristic direction of sheets.
$I_2=I_1{\cos }^2\theta \Rightarrow \left(\frac{1}{3}{I}_1\right)=I_1{\cos }^2\theta$
$\Rightarrow \theta ={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)\cong {55}^{\circ }$