Question

A beam of polarized light is sent into a system of two polarizing sheets. The polarizing direction of the first sheet is at an angle ? relative to the polarization direction of the incident light, and the second is at a right angle to the incident light. In terms of ?, what fraction of the incident intensity is transmitted by the two sheets?

Answer 1

let the intensity of incident polarized light be ''I_incident''

first sheet makes angle relative to incident light

so intensity emerging out from first

I_first = I_incident Cos²

second polariser make angle 90 with the incident light, hence the angle made relative to first polariser and hence the light coming from first polariser would be (90-)

intensity of light coming from second polariser

I_second = I_first Cos² (90-)

I_first = (I_incident Cos²) Sin²

fraction = I_second/I_incident = Cos² Sin²