Question

Two polaroids ‘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 unpolarized light incident on A?

Answer 1

Let θ_AC, angle between the transmission axis of Polaroid A and Polaroid C.

θ_CB, angle between the transmission axis of Polaroid C and Polaroid B.

Then,

θ_AC + θ_CB = 180° (As, Polaroid ‘A’ and ‘B’ are kept in crossed position.)

Or, θ_AC = 180° − θ_CB ... (1)

Intensity of unpolarized light = I₀

I₁, I₂ and I₃ are the intensities of light on passing through the A, B and C polarises respectively.

Now,

`I_1 = 1/2I_0   .....(2)`

`I_2 =I_1cos^2theta_(AC)`

   =`1/2I_0cos^2theta_(AC)`

`= 1/2I_0 cos^2(180° -theta_(CB))`  (from equation (1))

`I_2=1/2I_0sin^2theta_(CB)......... (3)`

and, `I_3 =I_2cos^2theta_(CB)`

`I_3=(1/2I_0sin^2theta_(CB)) cos^2theta_(CB)`

or,`I_3 = 1/2I_0sin_2theta_(CB)cos^2theta_(CB)`

As,given, `I_3=1/8 I_0`

Therefore,`1/8I_0 =1/2I_0 xx 1/4(sin2theta_(CB))^2`

`or,  sin 2 theta_(CB =1)`

`or, 2theta_(CB) =90°`

`or,  theta_(CB) =45°`

Thus, Polaroid ‘C’ must be placed at angle 45° with Polaroid ‘B’.