Question

A polaroid sheet ‘P’ is placed on another similar polaroid sheet ‘Q’ such that the angle between their axes is \(45^\circ\). - The ratio of the intensities of the light emerged from polaroid ‘Q’ and the unpolarised light incident on polaroid ‘P’ is

• A. \(1:4\)
• B. \(1:2\)
• C. \(1:\sqrt{3}\)
• D. \(1:\sqrt{2}\)

Hint:

Remember that when unpolarized light passes through a polaroid, its intensity is reduced by half. The second polaroid further reduces intensity based on Malus’s Law: \[ I = I_0 \cos^2 \theta \] where \(\theta\) is the angle between the two polaroid axes.

Answer 1

The Correct Option is A

- When unpolarized light passes through the first polaroid, its intensity becomes half: \[ I_1 = \frac{I_0}{2} \]
- After passing through the second polaroid, Malus’s law applies: \[ I_2 = I_1 \cos^2 \theta \]
- Given \( \theta = 45^\circ \), so: \[ \cos 45^\circ = \frac{1}{\sqrt{2}} \Rightarrow \cos^2 45^\circ = \frac{1}{2} \]
- Substitute values: \[ I_2 = \frac{I_0}{2} \times \frac{1}{2} \]
- Therefore: \[ I_2 = \frac{I_0}{4} \]
- Hence, the ratio of final to initial intensity is: 1 : 4