Question

An unpolarised light beam of intensity 2I₀ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

• A. \(\frac{I_0}{4}\)
• B. \(\frac{I_0}{2}\)
• C. \(\frac{3I_0}{4}\)
• D. \(\frac{3I_0}{2}\)

Answer 1

The Correct Option is C

To determine the intensity of light after passing through two polaroids, we apply Malus's Law. Here's a step-by-step explanation:

1. The initial light intensity is given as \(2I_0\). When unpolarized light passes through the first polaroid, its intensity is reduced by half. Hence, the intensity after the first polaroid \(P\) is: I_1 = \frac{2I_0}{2} = I_0
2. According to Malus's Law, the intensity \(I_2\) of light passing through a second polaroid \(Q\) is given by: I_2 = I_1 \cos^2 \theta where \(\theta\) is the angle between the passing axes of polaroids \(P\) and \(Q\). Here, \(\theta = 30^\circ\).
3. Substituting the known values, we have: I_2 = I_0 \cos^2 30^\circ = I_0 \left(\frac{\sqrt{3}}{2}\right)^2 = I_0 \times \frac{3}{4} = \frac{3I_0}{4}

Therefore, the intensity of the emergent light after passing through both polaroids is \(\frac{3I_0}{4}\).

Answer 2

The intensity of the emergent light,
\(I = I_0 × \frac{3}{4}\)
So, the correct option is (C): \( \frac{3I_0}{4}\)