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Discuss the intensity of transmitted lig...

Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?

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Let `I_(0)` be the intensity of polarised light after passing through the first polariser `P_1`. Then the intensity of light after passing through second polariser `P_2` will be
`I= I_(0) cos^(2) theta`, 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 `(pi"/"2- theta)`. Hence the intensity of light imerging from `P_(3)` will be
`I= I_(0) cos^(2) ((pi)/(2)-theta)= I_(0) cos^(2) theta sin^(2) theta= (I_(0)"/"4) sin^(2) 2theta`
Therefore, the transmitted intensity will be maximum when `theta= pi"/"4`.
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