Question

Unpolarized light of intensity $32 \, W \, m^{- 2}$ 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. $32 \, W \, m^{- 2}$
• B. $3 \, W \, m^{- 2}$
• C. $8 \, W \, m^{- 2}$
• D. $4 \, W \, m^{- 2}$

Answer 1

Answer: (B)

$I_{0}=32$

For 1st polaroid
$I_{1}=\frac{I_{0}}{2}$
For 2nd polaroid
$I_{2}=I_{1}cos^{2} \theta $
$I_{2}=\frac{I_{0}}{2}\times cos^{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}cos^{2} 60 ^\circ $
$I_{3}=I_{2}\times \frac{1}{4}$
$I_{3}=\frac{3}{8}I_{0}\times \frac{1}{4}$
$I_{3}=\frac{3 I_{0}}{32}$
$I_{3}=\frac{3}{32}\times 32$
$I_{3}=3Wm^{- 2}$