Question

Unpolarized light of intensity $I_0$ is incident on two polaroids placed coaxially. The transmission axis of the second polaroid is at an angle of $60^\circ$ to the first. The intensity of emerging light is:

• A. $I_0/2$
• B. $I_0/4$
• C. $I_0/8$
• D. $3I_0/8$

Hint:

First polaroid always reduces unpolarized intensity by exactly 50%. Then apply Malus's Law ($I = I_1\cos^2\theta$) for the second polaroid.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When unpolarized light passes through a polaroid, its intensity is reduced by half regardless of the orientation.
Subsequent passage through another polaroid (the analyzer) follows Malus' Law.
Key Formula or Approach:
1. Intensity after 1st polaroid: \( I_1 = I_0/2 \).
2. Malus' Law: \( I_2 = I_1 \cos^2 \theta \).
Step 2: Detailed Explanation:
Initial intensity = \( I_0 \).
After the first polaroid, light becomes plane polarized with intensity:
\[ I_1 = \frac{I_0}{2} \] This polarized light then hits the second polaroid oriented at \( \theta = 60^\circ \) to the first.
Using Malus' Law:
\[ I_{out} = I_1 \cos^2(60^\circ) \] Since \( \cos 60^\circ = 1/2 \), then \( \cos^2 60^\circ = 1/4 \).
\[ I_{out} = \left( \frac{I_0}{2} \right) \left( \frac{1}{4} \right) = \frac{I_0}{8} \] Step 3: Final Answer:
The final intensity is \( I_0/8 \).
This matches Option (C).