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Q.
When a Polaroid sheet is rotated between two crossed polaroids, the intensity of the transmitted will be maximum, when angle $\theta $ between pass axes is
NTA AbhyasNTA Abhyas 2020
Solution:
Let $I_{0}$ be the intensity of polarized light after passing through the first polarizer $P_{1}.$ Then the intensity of light after passing through second polarizer $P_{2}$ will be
$L=I_{0}cos^{2}q$
where $\theta $ is the angle between pass axes of $P_{1}$ and $P_{2}.$ since, $P_{1}$ and $P_{3}$ are crossed the angle between the pass axes of $P_{2}$ and $P_{3}$ will be $\left(\frac{\pi }{2} - \theta \right).$ Hence, the intensity of light emerging from $P_{2}$ will be
$I=I_{0}\left(cos\right)^{2}\theta \left(cos\right)^{2}\left(\frac{\pi }{2} - \theta \right)$
$I=I_{0}\left(cos\right)^{2}\theta \left(sin\right)^{2}\theta =\left(\frac{I_{0}}{4}\right)\left(sin\right)^{2}$
$2\theta $
Hence, transmitted intensity will be maximum,
when $\theta =\frac{\pi }{4}.$