Two polaroid `A and B` are kept in crossed position. How should a third polaroid `C` be placed between them so that the intensity of polarized light transmitted by polaroid `B` reduces to `(1)/(8)th` of the intensity of unplarised light incident on `A` ?

Two polaroid `A and B` are kept in crossed position. How should a thir

1.	Two polaroid `A and B` are kept in crossed position. How should a third polaroid `C` be placed between them so that the intensity of polarized light transmitted by polaroid `B` reduces to `(1)/(8)th` of the intensity of unplarised light incident on `A` ?
Answer» Correct Answer - `45^(@)` Let the angle between the pass axis of the polaroids `A` and `C` be `theta`. As polaroids `A` and `B` are crossed, the angle between the pass axes of polaroids `C` and `B` is `(90 - theta)`. When unpolaroids light of intensity `I_(0)` falls on first polaroid `A`, intensity of polarised light through `A` is `I_(1) = I_(0)//2`. This light falls on polaroid `C` at `/_ theta`. `:.` Intensity of light transmitted through `C` is `I_(2) = I_(1) cos^(2) theta = (I_(0))/(2)cos^(2) theta` Light transmitted from `C` falls on polaroid `B` at an angle `(90 - theta)`. Therefore, intensity of light transmitted from `B` is `I_(3) = I_(2)cos^(2)(90 - theta)` `= [(I_(0))/(2)cos^(2) theta]sin^(2)theta = (I_(0))/(2)(sin theta cos theta)^(2)` `I_(3) = (I_(0))/(8)(sin 2 theta)^(2)` As `I_(3) = I_(0)//8`, therefore, therefore `(sin 2 theta)^(2) = 1` `sin 2 theta = 1, or 2 theta = 90^(@) or theta = 45^(@)`

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Two polaroid `A and B` are kept in crossed position. How should a third polaroid `C` be placed between them so that the intensity of polarized light transmitted by polaroid `B` reduces to `(1)/(8)th` of the intensity of unplarised light incident on `A` ?

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