Question

Abeam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of ${45}^{\circ }$ relative to that of $A$. The intensity of the emergent light is :

• A. $\frac{I_0}{8}$
• B. $\frac{I_0}{4}$
• C. $I_0$
• D. $\frac{I_0}{2}$

Answer 1

The correct option is B $\frac{I_0}{4}$


Step 1: The intensity of light reduces to half of its initial value after passing through a Polaroid placed perpendicularly in its path.

Using Brewster law of ploaroid: $I=I_0{\cos }^2\theta$
$I=\frac{I_0}{2}$ ......(1)

Step 2: The second polaroid will reduce the intensity of light which is given by the square of the cosine of the angle at which it is oriented to the first polaroid.
$I^{\prime }=I{\cos }^2\theta$

Substitute the values,

$I^{\prime }=\frac{I_o}{2}{\cos }^{2}45$

$=\frac{I_0}{2}\times \frac{1}{2}=\frac{I_0}{4}$

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