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Two polaroids are kept crossed to each o...

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of `45^(@)` . The percentage of incident light now transmitted through the system is

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Initially the polaroids are crossed to each other that is the angle between their polarising directions is `90^(@)` when one is rotated through `60^(@)` then the angle between their polarising directions will become `30^(@)`
Let the intensity of the incident unpolarised light `=I_(0)`
Then the intensity of light emerging from the first polaroid is `I_(1)=(1)/(2)I_(0)` ltbr. this light is plane polarised and passes through the second polaroid.
The intensity of light emerging from the second polaroid is `I_(2)=I_(1)cos^(2)theta`
`theta=` the angle between the polarising directions of the two polaroids.
`I_(1)=(lamda)/(2)I_(0)" and "theta=30^(@)" so "I_(2)=I_(1)cos^(2)30^(@)=(1)/(2I_(0)cos^(2)30^(@()implies(I_(2))/(I_(0))=(3)/(8)` ltbr. `therefore` transmission percentage `=(I_(2))/(I_(0))xx100=(3)/(8)xx100=37.5%`
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