Question

An unpolarised light of intensity 32 w/m2 passes through three polarisers, such that the transmission axis of last polariser is crossed with that of that of the first. If the intensity of emergent light is 3 w/m2 , then the angle between the teansmission axes of the first two polarisers is

Answer 1

Since the light is unpolarized, after crossing the first polarizer the intensity will be 322=16W/m2. Now if the second polarizer is at an angle θ with first polarizer then the output from the second polarizer will be I2=I1cos2θ=16cos2θ. Now the angle between the second and third polarizer will be 90°−θ. Now After passing through the third polarizer the intensity will be I3=I2cos2(90−θ)=16 cos2θ sin2θ

Now we have
16 cos2θ sin2θ = 316cos2θ(1−cos2θ)=316cos2θ−16cos4θ=316cos4θ−16cos2θ+3=016x2−16x+3=0 (substuting x=cos2θ)x=14, 34  Hence cos2θ=14 or 34cosθ=12 or 3√2,θ=60° or 30°
So the angle can be either 60o or 30o.