Question

A beam of unpolarised light of intensity \( I_0 \) is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is:

• A. \(\frac{I_0}{2}\)
• B. \(\frac{I_0}{2\sqrt2}\)
• C. \(\frac{I_0}{4}\)
• D. \(\frac{I_0}{8}\)

Answer 1

The Correct Option is C

When unpolarised light passes through a polaroid, the intensity of the transmitted light \( I \) is given by:

\[ I = \frac{I_0}{2}, \]

where \( I_0 \) is the intensity of the incident unpolarised light.

Passing through Polaroid A: After passing through polaroid A, the intensity becomes:

\[ I_A = \frac{I_0}{2}. \]

Passing through Polaroid B: When the light passes through the second polaroid B at an angle \( \theta = 45^\circ \) relative to the first:

\[ I_B = I_A \cos^2(45^\circ) = \left( \frac{I_0}{2} \right) \cos^2(45^\circ). \]

Since \( \cos(45^\circ) = \frac{1}{\sqrt{2}} \):

\[ I_B = \left( \frac{I_0}{2} \right) \left( \frac{1}{\sqrt{2}} \right)^2 = \left( \frac{I_0}{2} \right) \left( \frac{1}{2} \right) = \frac{I_0}{4}. \]

Thus, the intensity of emergent light after passing through both polaroids is:

\[ \frac{I_0}{4}. \]