Question

A polaroid \(P\) is placed between two crossed polaroids \(Q\) and \(R\) such that when unpolarised light is incident on \(Q\), it emerges from \(R\) with maximum possible intensity. The ratio of intensity of unpolarized light incident on \(P\) and the intensity of polarized light emerging from \(R\) is

• A. \(4:1\)
• B. \(2:1\)
• C. \(3:1\)
• D. \(1:1\)

Hint:

For crossed polaroids, maximum transmission is obtained when the middle polaroid is placed at \[ \boxed{45^\circ} \] to both. Apply Malus' law successively: \[ \boxed{I=I_0\cos^2\theta.} \]

Answer 1

The Correct Option is A

Step 1: Find the intensity after the first polaroid. Let the intensity of the unpolarized light incident on \(Q\) be \[ I_0. \] After passing through \(Q\), \[ I_1=\frac{I_0}{2}. \] This is the intensity incident on the middle polaroid \(P\).

Step 2: Apply Malus' law. For maximum transmitted intensity through two crossed polaroids, the axis of \(P\) should make an angle \[ 45^\circ \] with each polaroid. After passing through \(P\), \[ I_2 = I_1\cos^245^\circ = \frac{I_1}{2}. \] After passing through \(R\), \[ I_3 = I_2\cos^245^\circ = \frac{I_1}{4}. \] Since \[ I_1=\frac{I_0}{2}, \] we get \[ I_3=\frac{I_0}{8}. \]

Step 3: Find the required ratio. The intensity incident on \(P\) is \[ I_1=\frac{I_0}{2}. \] The intensity emerging from \(R\) is \[ I_3=\frac{I_0}{8}. \] Therefore, \[ I_1:I_3 = \frac{I_0}{2}:\frac{I_0}{8} = 4:1. \] Hence, \[ \boxed{4:1}. \] Thus, \[ \boxed{(A)} \] is the correct answer.