Question

An unpolarized light is incident on a system of two crossed polaroids $A$ and $B$. Now the second polaroid $B$ is rotated by, $30^{\circ}$ towards $A$. Percentage of light transmitted through the system is

• A. $50 \%$
• B. $30 \%$
• C. $25 \%$
• D. $12.5 \%$

Answer 1

Answer: (D)

$12.5 \%$

Answer 2

Let $I_0$ be intensity of incident unpolarised light. Then the intensity of light emerging from the first polaroid will be $I_1 = \frac{I_0}{2} .$
Intensity of transmitted light is given by $I = I_0 \, \cos^2 \theta \, \, \, \, \, \,$ (Malus' law)
where 8 = angle between polaroids.
Now, polaroid is rotated through $30^{\circ}$ .
So angle between two polaroids $\theta = 90^{\circ} - 30^{\circ} = 60^{\circ}$
$\theta \, \, I' = I_1 \cos^2 60^{\circ} = \frac{I_0}{8}$
Percentage of light transmitted through the system,
$= \frac{I'}{I_0} \times 100 \% = \frac{1}{8} \times 100 \%$
$= 12.5 \%$