Question

An unpolarized beam of intensity \( I_0 \) is incident on a pair of Nicol’s prism making an angle of 60 degrees with each other. The intensity of the light emerging from the pair is

• A. \( I_0 \)
• B. \( I_0/2 \)
• C. \( I_0/4 \)
• D. \( I_0/8 \)

Hint:

In polarizer problems, always remember that the intensity of light is halved after passing through the first polarizer, and further reduced by the square of the cosine of the angle between the polarizers.

Answer 1

The Correct Option is C

Step 1: Understanding the phenomenon.
The problem involves light passing through two Nicol's prisms. When unpolarized light passes through a polarizer, the intensity of the transmitted light becomes half of the initial intensity. When it passes through a second polarizer, the intensity further reduces depending on the angle between the polarizer axes. In this case, the angle between the prisms is 60 degrees.

Step 2: Intensity after first polarizer.
When unpolarized light passes through the first Nicol’s prism, the intensity reduces to half of the initial intensity: \[ I_1 = \frac{I_0}{2} \]
Step 3: Intensity after the second polarizer.
The second polarizer makes an angle of 60 degrees with the first. The intensity of light emerging from the second polarizer is given by: \[ I_2 = I_1 \cos^2 \theta = \frac{I_0}{2} \cos^2 60^\circ \] Since \( \cos 60^\circ = 0.5 \), we get: \[ I_2 = \frac{I_0}{2} \times \left(0.5\right)^2 = \frac{I_0}{4} \]
Step 4: Conclusion.
Thus, the intensity of the light emerging from the pair is \( \frac{I_0}{4} \). Therefore, the correct answer is (3) \( I_0/4 \).