Question

Unpolarized light of intensity $I$ passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be $\frac{I}{2}$. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be $\frac{I}{8}$. The angle between polarizer A and C is:

• A. $45°$
• B. $60°$
• C. $0°$
• D. $30°$

Answer 1

The correct option is A

$45°$

Step 1: Given

The initial intensity of light: $I$

The intensity of light after A: $I_1=\frac{I}{2}$

The intensity of light after B: $I_2=\frac{I}{2}$

The intensity of light after B when C is also placed: $I_3=\frac{I}{8}$

Step 2: Formula Used

Malus Law Formula: $I=I_0{\cos }^2\theta$

Step 3: Find the angle between A and C

When light passes through a polariser its intensity becomes half. Here, when the light passes through A its intensity becomes half and again when it passes through B its intensity remains same as after passing through A. This implies that A and B are parallel to each other. Now, find an expression after light passes through C using Malus law.

$\begin{array}{rcl}{I}_{afterC}& =& I_1{\cos }^2\theta \\ & =& \frac{I}{2}{\cos }^2\theta \end{array}$

Calculate the value of angle using Malus law and substituting values

$$\begin{gathered} I_3=I_{afterC}{\cos }^2\theta \\ \frac{I}{8}=\left(\frac{I}{2}{\cos }^2\theta \right){\cos }^2\theta \\ {\cos }^4\theta =\frac{1}{4} \\ \cos \theta =\frac{1}{\sqrt{2}} \\ \theta =45° \end{gathered}$$

Hence, the angle between polariser A and C is $45°$.