Question

Two polaroide $A$ and $B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other Now, another polaroid $C$ is placed between $A$ and $B$ bisecting angle between them If intensity of unpolarized light is $I _0$ then intensity of transmitted light after passing through polaroid $B$ will be:

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

Hint:

The intensity of light passing through successive polarising filters is given by the product of intensity and the cosine square of the angle between the polarising axes.

Answer 1

The Correct Option is A

$I_A=\frac{I_o}{2}$
$IC=\frac{I_o}{2}{\cos }^{2}45=\frac{I_o}{4}$
$I_B=I_C{\cos }^{2}45=\frac{I_o}{8}$

Answer 2

The intensity after passing through polaroid A is:

\[ I_A = \frac{I_0}{2} \]

The intensity after passing through polaroid C, with the angle between A and C being 45°, is:

\[ I_C = I_A \cos^2 45^\circ = \frac{I_0}{2} \times \frac{1}{2} = \frac{I_0}{4} \]

The intensity after passing through polaroid B, with the angle between C and B being 45°, is:

\[ I_B = I_C \cos^2 45^\circ = \frac{I_0}{4} \times \frac{1}{2} = \frac{I_0}{8} \]