Elliptical partially polarized beam and its intensity

[mogul28]

Homework Statement

A partially elliptically polarized beam of light, propagating int he z direction, passes through a perfect linear polarization analyzer. When the transmission axis of the analyzer is along the x direction, the transmitted intensity is maximum and has the value of 1.5 I[0]. When the transmission is along the y direction, the transmitted intensity is minimum and has the value of I[0].
(a) What is the intensity when the transmission axis makes angle θwith the x-axis? Does your answer depend on what traction of the light is unpolarized?
(b) The original beam is made to pass first through a quarter-wave plate and then through the linear polarization analyzer. The quarter-wave plate has its axes lined up with the x and y axes. It is now found that the maximum intensity is transmitted through the two devices when the analyzer transmission axis makes an angle of 30° witht the x-axis.
Determine what is this maximum intensity is and determine the fraction of the incident intensity which is unpolarized.

Homework Equations

The Attempt at a Solution

first i found V and then used it to find fractional polarization then
I= I[max]((1+pcos2phi)/(1+p))
but I'm lost at b since i don't know how to apply quarter wave plate information to get teh I[max]

 

[mark726]

(a) To find the intensity when the transmission axis makes an angle θ with the x-axis, we can use the equation I = I[0]*cos^2(θ). This means that the intensity will depend on the angle θ, as well as the initial intensity I[0]. The answer does not depend on what fraction of the light is unpolarized.

(b) To find the maximum intensity transmitted when the analyzer transmission axis makes an angle of 30° with the x-axis, we can use the equation I = I[0]*(1+pcos2φ)/(1+p), where p is the fractional polarization. In this case, we know that the quarter-wave plate has its axes lined up with the x and y axes, so the angle φ is 45°. We also know that the maximum intensity is transmitted, so we can set I = I[max] and solve for p. Once we have p, we can plug it back into the equation to find the maximum intensity transmitted. To determine the fraction of the incident intensity which is unpolarized, we can use the equation I[unpolarized] = I[0]*(1-p).