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

Answer: (D)

$45^\circ$

Answer 2

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: $45^\circ$