Question

Two polaroids are crossed to each other. When one of them is rotated through ${60}^{\circ }$, then what percentage of the incident unpolarised light will be transmitted by the polaroids?

• A. $37.5\%$
• B. $50\%$
• C. $66.5\%$
• D. $100\%$

Answer 1

The correct option is A $37.5\%$

When the direction of polarization of two polarizers are at ${90}^{\circ }$ with each other, they are said to be crossed. In that case, no light passes through to the other side.

In the question, initially the polarizers were crossed. Suppose the first polarizer is rotated by ${60}^{\circ }$ with its intial direction.


Now, the first polarizer makes an angle of ${30}^{\circ }$ with the second polarizer.

Suppose unpolarized light from the sun is incident at the first polarizer with intensity $I$. Then linearly polarized light coming out of the polarizer 1 has intensity $\frac{I}{2}$.

After the linearly polarized light passes through the 2nd polarizer, intensity $I_2$ is given by
$I_2=I_1{\cos }^2\varphi =\frac{I}{2}{\cos }^2{30}^{\circ }$
$=\frac{I}{2}\times \frac{3}{4}=\frac{3I}{8}$

So % of initial unpolarized light transmitted
$=\frac{3I/8}{I}\times 100=37.5\%$