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Question:

Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other. Unpolarised light of intensity I0 is incident on P1. A third Polaroid P3 is kept in between P1 and P2 such that its pass axis makes an angle of 30° with that of P1. Determine the intensity of light transmitted through P1, P2, and P3.

Solution:

Intensity of light passing through a single polaroid is halved when unpolarized light is incident on it.
Hence, I1 = I0/2
Now, the angle between P1 and P2 is 30°.
By Malus' Law, I2 = I1cos²(φ) = I1cos²(30°) = (3I0)/8
Angle between P2 and P3 is 60°.
By Malus' Law, I3 = I2cos²(φ) = I2cos²(60°) = (3I0)/16