Question

In an experiment, two polaroids are arranged such that the intensity of the polarised light emerged from the second polaroid is 37.5% of the intensity of the unpolarised light incident on the first polaroid. Then the angle between the axes of the two polaroids is

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

Hint:

When light passes through two polaroids, apply Malus' Law: \( I = I_0 \cos^2 \theta \), and remember the first polaroid halves the unpolarized light's intensity.

Answer 1

The Correct Option is D

Step 1: When unpolarized light passes through the first polaroid, intensity becomes: \[ I_1 = \frac{I_0}{2} \] Step 2: When this light passes through the second polaroid at angle \( \theta \), the intensity becomes: \[ I_2 = I_1 \cos^2 \theta = \frac{I_0}{2} \cos^2 \theta \] Step 3: Given \( I_2 = 0.375 I_0 \), so: \[ \frac{I_0}{2} \cos^2 \theta = 0.375 I_0 \Rightarrow \cos^2 \theta = 0.75 \Rightarrow \cos \theta = \sqrt{0.75} = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2} \Rightarrow \theta = 30^\circ \]