Two Polaroids are placed in the path of an unpolarized beam of intensity I0 such that no light is emitted from the second polaroid. If a third Polaroid whose polarization axis makes an angle θ with the polarization axis of first Polaroid, is placed between these Polaroids then the intensity of light emerging from the last Polaroid will be
Question
Two Polaroids are placed in the path of an unpolarized beam of intensity I0 such that no light is emitted from the second polaroid. If a third Polaroid whose polarization axis makes an angle θ with the polarization axis of first Polaroid, is placed between these Polaroids then the intensity of light emerging from the last Polaroid will be
Solution
The intensity of light that passes through the first polaroid is reduced by half, so it becomes I0/2.
When the light passes through the third polaroid, which is at an angle θ to the first, the intensity is reduced by a factor of cos²θ. So the intensity becomes I0/2 * cos²θ.
Finally, the light passes through the second polaroid, which is aligned with the first one. Since the third polaroid was at an angle θ to the first, it is also at an angle θ to the second. Therefore, the intensity is again reduced by a factor of cos²θ.
So the final intensity of the light emerging from the last polaroid is I0/2 * cos²θ * cos²θ = I0/2 * cos⁴θ.
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