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 $\theta $ 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 $\theta = 45^\circ $ and minimum when $\theta = 0^\circ $

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