Question

The diagram shows four pairs of polarizing sheets, with the polarizing directions indicated by dashed lines. The two sheets of each pair are placed one behind the other, and the front sheet is illuminated by unpolarized light. The incident intensity is the same for all pairs of sheets. Rank the pairs according to the intensity of the transmitted light, least to greatest.

• A. $1,2,3,4$
• B. $4,2,1,3$
• C. $2,4,3,1$
• D. $2,1,4,3$

Answer 1

The correct option is D $2,1,4,3$

Let $I_0$ be the intensity of unpolarized light.

The intensity of light after passing through the first Polaroid of each pair $=\frac{I_0}{2}$.

Intensity of light after passing through second Polaroid of each pair

$I=\frac{I_0}{2}{\cos }^2\theta$

Where, $\theta =$ angle between the transmission axis of two Polaroids

For $\text{Pair 1}:$ $\theta ={60}^{\circ }$

$\therefore I_1=\frac{I_0}{2}{\cos }^2{60}^{\circ }=\frac{I_0}{8}=0.125I_o$

For $\text{Pair 2}:$ $\theta ={90}^{\circ }$

$\therefore I_2=0$

For $\text{Pair 3}:$ $\theta ={30}^{\circ }$

$\therefore I_3=\frac{I_0}{2}{\cos }^2{30}^{\circ }=\frac{3I_0}{8}=0.375I_o$

For $\text{Pair 4}:$ $\theta ={45}^{\circ }$

$\therefore I_4=\frac{I_0}{2}{\cos }^2{45}^{\circ }=\frac{I_0}{4}=0.25I_o$

Ascending order of intensities
$I_2<I_1<I_4<I_3$

Hence, the correct option is $\left(\text{D}\right)$.