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

Answer: (C)

$\frac{I_0}{4}$

Answer 2

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:

$\frac{I_0}{4}.$