Polarization — Question 4

Question 4

Analyzer extrema measure the linearly polarized part of a mixture

A beam is an incoherent sum of x-polarized intensity Ip and unpolarized intensity Iu. A rotating ideal analyzer records a maximum of 7.0 W/m squared and a minimum of 2.0 W/m squared.

1. Derive the analyzer intensity and infer Ip and Iu.

2. Find total incident intensity and the degree of linear polarization, defined as Ip divided by the total.

Question 4 - Solution

Analyzer extrema measure the linearly polarized part of a mixture

(a) Method and calculation

$$I(\theta)=I_p\cos^2\theta+I_u/2,\quad I_{\max}=I_p+I_u/2,\ I_{\min}=I_u/2.$$$$\boxed{I_p=I_{\max}-I_{\min}=5.0\,\mathrm{W/m^2},\quad I_u=2I_{\min}=4.0\,\mathrm{W/m^2}}.$$

(b) Interpretation and further calculation

$$\boxed{I_{\mathrm{in}}=I_{\max}+I_{\min}=9.0\,\mathrm{W/m^2}}.$$$$\boxed{\mathcal P_L=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}=5/9}.$$

Physical check

The minimum is half the unpolarized component, not the entire unpolarized incident intensity.