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?

Answer 1

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°