Question

A point source \(S\) emits unpolarized light uniformly in all directions. At two points A and B, the ratio \(r = I_A/I_B\) of the intensities of light is \(2\). If a set of two polaroids having 45° angle between their pass-axes is placed just before point B, then the new value of r will be ____

Answer 1

Correct Answer: 8

Case-I: Without Polaroids 

The source emits unpolarised light, and the given intensity ratio is:

\[ r = \frac{I_A}{I_B} = 2 \]

Case-II: With Polaroids at Point B

When the first polaroid is introduced, the intensity of light becomes:

\[ I'_B = \frac{I_B}{2} \]

When the second polaroid is introduced at 45° relative to the first, the intensity of light becomes:

\[ I''_B = I'_B \cdot \cos^2(45^\circ) = \frac{I_B}{2} \cdot \frac{1}{2} = \frac{I_B}{4} \]

New Intensity Ratio

The new intensity ratio is:

\[ r' = \frac{I_A}{I''_B} = \frac{I_A}{\frac{I_B}{4}} = 4 \cdot \frac{I_A}{I_B} = 4 \times 2 = 8 \]

Final Answer:

r = 8