Question

A beam 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° relative to that of A. The intensity of emergent light is:

• A. \(\frac{I_0}{2}\)
• B. \(\frac{I_0}{2\sqrt2}\)
• C. \(\frac{I_0}{4}\)
• D. \(\frac{I_0}{8}\)

Answer 1

The Correct Option is C

The intensity of transmitted unpolarised light \( I \) after passing through a polaroid is \( I = \frac{I_0}{2} \), where \( I_0 \) is the incident intensity.

Polaroid A: The intensity after passing through polaroid A is \( I_A = \frac{I_0}{2} \).

Polaroid B: When the light passes through polaroid B, oriented at an angle \( \theta = 45^\circ \) to polaroid A, the intensity is \( I_B = I_A \cos^2(45^\circ) = \left( \frac{I_0}{2} \right) \cos^2(45^\circ) \).

Given that \( \cos(45^\circ) = \frac{1}{\sqrt{2}} \), the intensity is:

\[ I_B = \left( \frac{I_0}{2} \right) \left( \frac{1}{\sqrt{2}} \right)^2 = \left( \frac{I_0}{2} \right) \left( \frac{1}{2} \right) = \frac{I_0}{4}. \]

Therefore, the final intensity of the light after passing through both polaroids is \( \frac{I_0}{4} \).