Unpolarised light of intensity `32 Wm^(-2)` passes through three polarisers such that the transmission axis of the last polariser is crossed with the first. If the intensity of the emerging light is `3W m^(-2)` What is the angle between the tranmission axes of the first two polarisers ?

Explanation

Intensity of unpolarised light `(I_(0))=32W//m^(2)` , Intensity of emergent light `(I_(3))=2 W//m^(2)`
As we know intensity of unpolarised light becomes half after passing first polarizer i.e., `I_(1)=16 W//m^(2) …(i)`
After passing second polarizer `I_(2)=16cos^(2) theta`
After third polarizer `I_(3)=(16 cos^(2) theta) sin^(2) theta`
`rArr 3=16 cos^(2) theta sin^(2) theta rArr (sin 2theta)^(2)=3/4`
`rArr sin 2 theta=sqrt3/2 rArr 2 theta=pi/3 rArr theta=pi/6`