Question

Unpolarised light of intensity $32\, Wm^{-2}$ passes through three polarisers such that the transmission axis of the last polariser is crossed with first. If the ensity of the emerging light is $3\, Wm^{-2}$ the angle between the axes of the first two polarisers is.

• A. $45^\circ$
• B. $60^\circ$
• C. $30^\circ$
• D. zero

Answer 1

Answer: (C)

Since unpolarized light is passing through the first polarizer, hence the intensity of light after crossing the first polarizer will be
$I_{1}=\frac{1}{2}I_{0}=16Wm^{- 2}$
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}cos^{2}\theta =16cos^{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 $
$\Rightarrow I_{3}=16cos^{2}\theta sin^{2}\theta =3$
$\Rightarrow 4cos^{2}\theta sin^{2}\theta =\frac{3}{4}$
$\Rightarrow \left(sin\right)^{2}\left(2 \theta \right)=\frac{3}{4}$
$\theta =30^\circ $