Q: Unpolarized light of intensity 32 Wm-2 passes through three polarizers such that the transmission axis of the last polarizer is crossed with the first. If the intensity of the emerging light is 3 Wm-2, what is the angle between the transmission axes of the first two polarizers ? At what angle will the transmitted intensity be maximum?
Sol: If θ is the angle between the transmission axes of first Polaroid P1 and second P2 while φ between the
transmission axes of second Polaroid P2 and third P3 , then according to give problem.
φ = (90° – θ) … (i)
Now id I_0 is the intensity of Unpolarized light incident on Polaroid P_1, the intensity of light transmitted through it,
I1 = I0/2 = (32)/2 = 16 W/m2 … (ii)
Now as angle between transmission axes of polaroids P1 and P2 is θ , in a accordance with Malus law, intensity of light transmitted through P2 will be
I2 = I1 cos2 θ = 16 cos2 θ …. (iii)
And as angle between transmission axes of P2 and P3 is φ , light transmitted through P3 will be
I3 = I2 cos^2 φ = 16 cos2 θ cos2 φ … (iv)
According to give problem, I3 = 3 W/ m2
So, 4(sin 2θ)2 = 3
i.e., sin 2 θ = (√3/2)
or, 2 θ = 60°, i.e., θ = 30°.