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Unpolarized light is intensity I(0) pass...

Unpolarized light is intensity `I_(0)` passes through two polaroids `P_(1)` and `P_(2)` such that pass axis of `P_(2)` makes an angle `theta` with the pass axis of `P_(1)`. A third polaroid `P_(3)` is placed between `P_(1)` and `P_(2)` with pass axis of `P_(3)` making an angle `beta` with that of `P_(1)`. If `I_(1), I_(2), I_(3)` represent intensities of light trnasmitted by `P_(1), P_(2), P_(3)`, determine the values of angle `theta` and `beta` for which `I_(1) = I_(2) = I_(3)`.

Text Solution

Verified by Experts

Here,
`I_(1) =` intensity of light transmitted by `P_(1)`
`I_(3) =` intensity of light transmitted by `P_(3)`
`= I_(1) cos^(2) beta`
`I_(2) =` intensity of light transmitted by `P_(2)`
`= I_(3) cos^(2) (theta - beta)`
As `I_(2) = I_(3) :. cos^(2) (theta - beta) =1`
`cos (theta - beta) = 1 = cos 0^(@) :. theta = beta`
Also, `I_(1) = I_(2) = I_(1) cos^(2) beta cos^(2)(theta - beta)`
`= I_(1) cos^(2) beta cos^(2)0`
`cos^(2) beta = 1`, Hence `theta = beta = 0` or `pi rad`.
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