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The optic axis of two polaroids are incl...

The optic axis of two polaroids are inclined at an angle of `45^(@)` with each other. Unpolarised light of intensity `I_(0)` being incident on the first polaroid emerges from the second polaroid. Find the intensity of the emergent light.

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Int the first polaroid, the component of incident unpolarised light having polarisation parallel to the optic axis is transmitted through the polaroid and the perpendicular component is absorbed. So the intensity of light incident on the second polaroid `= (I_(0))/(2)`
Again, intensity of light `prop` `("amplitude of light" )^(2)`
If the amplitude of light incident on the second polaroid is `E_(0)`, then the amplitude of light having polarisation along its optic axis
`= E_(0) cos45^(@) = (E_(0))/(sqrt(2))`
[ `therefore` the angle between the optic axes = `45^(@)` So the intensity of light transmitted through the second polaroid is `((1)/(sqrt(2)))^(2) or (1)/(2)` of the intensity of light incident on it.
Hence the intensity of the emergent light `=(1)/(2)cdot (I_(0))/(2) = (I_(0))/(4)`
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