# Relative intensity of polarized and unpolarized light in incident beam

1. Jun 6, 2010

### nanobanano

1. A beam of light is a mixture of polarized light and unpolarized light. When it is sent through a Polaroid sheet, we find that the transmitted intensity can be varied by a factor of five depending on the orientation of the Polaroid. Find the relative intensities of these two components of the incident beam.

2. Relevant equations:
unpolarized light: I' = 1/2*Io'
polarized light: I = Iocos^2(Φ)

3. The attempt at a solution:
The intensity of transmitted unpolarized light will always be 1/2 the incident beam's intensity since it does not depend on the orientation of the Polaroid. The greatest the intensity of transmitted light from a polarized beam is equal to the intensity of the incident beam I = Io (when the axis of transmission is parallel to the electric field component). Since the two transmitted beams can vary by a factor of five, I've set 5I' = I and then substituted the equations for each (with the polarized intensity being equal to the incident beam intensity) resulting in Io' = 10*Io.