How does an unpolarised light get polarised when passed through a… - Vidyadip

Question

How does an unpolarised light get polarised when passed through a polaroid?
Two polaroids are set in crossed positions. A third polaroid is placed between the two making an angle θ with the pass axis of the first polaroid. Write the expression for the intensity of light transmitted from the second polaroid. In what orientations will the transmitted intensity be (i) minimum and (ii) maximum?

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Answer

A polaroid consists of long chain molecules aligned in a particular direction. The electric vectors (associated with the propagating light wave) along the direction of the aligned molecules get absorbed. Thus, if an unpolarised light wave is incident on such a polaroid, then the light wave will get linearly polarised with the electric vector oscillating along a direction perpendicular to the aligned molecules.
Expression for the intensity transmitted through second Polaroid:
$\text{l} = \text{(I}_{0}\cos^{2}\theta)\cos^{2}(90^{0} - \theta) = \text{I}_{0}(\cos\theta\sin\theta)^{2} = \text{I}_{0}\sin^{2}2 \theta/ 4 $
Where $I_0$ is the intensity of the polarized light after passing through the first polaroid.
Intensity will be maximum when θ = 45° and minimum when θ = 0°

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