Question

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

• A. \(60^\circ\)
• B. \(30^\circ\)
• C. \(90^\circ\)
• D. \(45^\circ\)

Answer 1

The Correct Option is D

Let \( I_0 \) be the intensity of unpolarized light incident on the first polaroid.

- The transmitted light intensity after passing through the first polaroid is:

\(I_1 = \frac{I_0}{2}.\)

- The intensity after passing through the second polaroid at an angle \( \theta \) is:

\(I_2 = I_1 \cos^2 \theta = \frac{I_0}{2} \cos^2 \theta.\)

- Similarly, for the third polaroid rotated by \( 90^\circ - \theta \), the transmitted intensity is:

\(I_3 = I_2 \cos^2 (90^\circ - \theta) = \frac{I_0}{2} \cos^2 \theta \sin^2 \theta.\)

- The intensity will be maximum when \( \sin 2\theta = 1 \), which occurs at \( \theta = 45^\circ \).

The Correct answer is: \(45^\circ\)