Let I0 be intensity of unpolarised light incident on first polaroid. I1= Intensity of light transmitted from 1st polaroid =
I0
2
θ be the angle between 1st and 2nd polaroid ϕ be the angle between 2nd and 3rd polaroid θ+ϕ=90∘ (as 1st and 3rd polaroid are crossed) ϕ=90∘−θ I2= Intensity from 2nd polaroid I2=I1cos2θ=
I0
2
cos2θ I3= Intensity from 3rd polaroid I3=I2cos2φ I3=I1cos2θcos2ϕ I3=
I0
2
cos2θcos2ϕ ϕ=90−θ I3=
I0
2
cos2θsin2θ I3=
I0
2
[
2sinθcosθ
2
]2 I3=
I0
8
sin22θ I3 will be maximum when sin2θ=1 2θ=90∘ θ=45∘