Question

Four polaroids are placed such that the optic axis of each is inclined at an angle of ${30}^{\circ }$ with the optic axis of the preceding one. If unpolarized light of intensity $I_0$ falls on the first polaroid, the light transmitted from the fourth polaroid is,

• A. $I_0$
• B. $\frac{I_0}{16}$
• C. $0.21I_{\circ }$
• D. None of the above

Answer 1

The correct option is C $0.21I_{\circ }$

When unpolarized light $I_0$ passes throgh the polariser, the intensity of transmitted light is $\frac{I_0}{2}$, irrespective of the polariser
So, after first polaroid, $I_1=\frac{I_0}{2}$

According to Malus' law,

After second polaroid,

$I_2=I_1{\cos }^2{30}^{\circ }=\frac{I_0}{2}\times \frac{3}{4}=\frac{3I_{\circ }}{8}$

After third polaroid,

$I_3=I_2{\cos }^2{30}^{\circ }=\frac{3I_{\circ }}{8}\times \frac{3}{4}=\frac{9I_{\circ }}{32}$

After fourth polaroid,
$I_4{\cos }^2{30}^{\circ }=\frac{9I_{\circ }}{32}\times \frac{3}{4}=\frac{27}{128}{I}_{\circ }=0.21I_0$

Hence, $\left(C\right)$ is the correct answer.