Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?
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Suppose `I_(0)` is intensity of polarised light after passing through the first polariser `P_(1)`. If `theta` is the angle between axes of `P_(1)` and polaroid sheet `P_(2)`, the intensity of polarised light after passing through `P_(2)` will be `I = I_(0) cos^(2) theta` ,br. As `P_(1)` and `P_(3)` are crossed, the angle between axes of `P_(1) and P_(3)` is `90^(@)`. Therefore, angle between axes of `P_(2) and P_(3) = (90^(@) - theta)`. The intensity of light emerging form `P_(3)`will be `I = [I_(0) cos^(2) theta] cos^(2)(90 - theta) = I_(0) cos^(2) theta sin^(2) theta` `= (I_(0))/(4)(4cos^(2) theta sin^(2) theta) = (I_(0))/(4) (2 sin theta cos theta)^(2)` `I = (I_(0))/(4)sin^(2) 2 theta` The intensity of polarised light transmitted from `P_(3)` will be maximum, when `sin 2 theta = max. = 1 = sin 90^(@)` `2 theta = 90^(@) or theta = (90)/(2) = 45^(@)`
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