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 find the intensity of the emergent light after passing through two polaroids, we need to use Malus's Law, which describes how the intensity of light changes as it passes through a polarizer.

Initially, the given beam is unpolarized and has an intensity of \(2I_0\). When unpolarized light passes through a polaroid, its intensity is reduced by half due to the nature of polarization. Therefore, after passing through the first polaroid \(P\), the intensity of light becomes:

I_1 = \frac{1}{2}(2I_0) = I_0

Next, the light passes through the second polaroid \(Q\), which is oriented at an angle of 30° with respect to the axis of the polaroid \(P\). According to Malus's Law, the intensity \(I_2\) of the light emerging from the second polaroid is given by:

I_2 = I_1 \cos^2 \theta

where \(\theta = 30^\circ\). Calculating this:

\cos 30^\circ = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}

Therefore, substituting into the formula we get:

I_2 = I_0 \left( \frac{\sqrt{3}}{2} \right)^2 = I_0 \cdot \frac{3}{4} = \frac{3I_0}{4}

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

The correct answer is therefore: \(\frac{3I_0}{4}\).