Question

Unpolarized light of intensity $32W{m}^{-2}$ passes through three polarizers such that transmission axes of the first and second polarizer make an angle $30^{\circ }$ with each other and the transmission axis of the last polarizer is crossed with that of the first. The intensity of the final emerging light will be

• A. $32W{m}^{-2}$
• B. $3W{m}^{-2}$
• C. $8W{m}^{-2}$
• D. $4W{m}^{-2}$

Answer 1

Answer: (B)

$I_0=32$

For 1st polaroid
$I_1=\frac{I_0}{2}$
For 2nd polaroid
$I_2=I_{1}co{s}^2\theta$
$I_2=\frac{I_0}{2}\times co{s}^{2}30^{\circ }$
$I_2=\frac{I_0}{2}\times \frac{3}{4}$
$I_2=\frac{3}{8}{I}_0$
As last crosses with 1st polarizer, hence angle between 2nd & last polariser is $60^{\circ }$
$I_3=I_{2}co{s}^{2}60^{\circ }$
$I_3=I_2\times \frac{1}{4}$
$I_3=\frac{3}{8}{I}_0\times \frac{1}{4}$
$I_3=\frac{3I_0}{32}$
$I_3=\frac{3}{32}\times 32$
$I_3=3W{m}^{-2}$