Question

An unpolarised beam of light incidents on a group of three polarising sheets arranged such that the angle between the axes of any two adjacent sheets is $30^\circ$. The ratio of the intensities of polarised light emerging from the second and third sheets is

• A. $1 : 1$
• B. $2 : 1$
• C. $4 : 3$
• D. $3 : 2$

Hint:

When multiple polarisers are used, the intensity after each depends on the square of the cosine of the angle between adjacent polarisers.

Answer 1

The Correct Option is C

Step 1: Light intensity after first polariser Unpolarised light passing through the first polariser: \[ I_1 = \frac{I_0}{2} \] Step 2: Light intensity after second polariser Angle between first and second: \(30^\circ\) \[ I_2 = I_1 \cos^2(30^\circ) = \frac{I_0}{2} \cdot \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3I_0}{8} \] Step 3: Light intensity after third polariser Angle between second and third: \(30^\circ\) \[ I_3 = I_2 \cos^2(30^\circ) = \frac{3I_0}{8} \cdot \left(\frac{\sqrt{3}}{2}\right)^2 = \frac{9I_0}{32} \] Step 4: Ratio of intensities from second and third polarisers \[ \frac{I_2}{I_3} = \frac{3I_0/8}{9I_0/32} = \frac{3}{8} \cdot \frac{32}{9} = \frac{4}{3} \]