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Question
An unpolarised light of intensity 32 Wm-2 passes through three Polaroids such that the axes of the first and the last Polaroids are at 90°. What is the angle between the axes of the first and middle Polaroids so that the emerging light has an intensity of only 3 Wm-2?
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Solution
Given: I = 3 Wm-2, I0 = 32Wm-2, θ = ?
∴ `"I"_circ = "KA"^2`
I = K AR2
I = `("K A"^2)/2 cos^2 theta sin^2 theta`
`"A"_"R" = "A"/sqrt2 cos theta sin theta`
`"I" prop "AR"^2`
I = `"I"_0/2 4/4 cos^2theta sin^2theta`
I = `"I"_0/8 (2 cos theta sin theta)^2`
I = `"I"_0/8 (sin 2 theta)^2`
`3 = 32/8 (sin 2 theta)^2`
`(sin 2 theta)^2 = 3/4`
`(sin 2 theta) = sqrt3/2`
2θ = 60°
θ = 30°
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