Polarization by Reflection — Question 10

Question 10

Reflected power and polarization together test whether incidence is Brewster

An unpolarized beam strikes a lossless dielectric interface. Measurements show total reflected power fraction R=0.080 and reflected degree of linear polarization D=0.75, with the s component stronger. Define $D=(P_{r,s}-P_{r,p})/(P_{r,s}+P_{r,p})$.

1. Infer the separate s and p power reflectances of the interface.

2. Find the minimum reflected power fraction after an ideal analyzer and decide whether the measurement is consistent with exact Brewster incidence.

Question 10 - Solution

Reflected power and polarization together test whether incidence is Brewster

(a) Method and calculation

$$R=(R_s+R_p)/2,\quad D=(R_s-R_p)/(R_s+R_p).$$$$\boxed{R_s=R(1+D)=0.140,\quad R_p=R(1-D)=0.020}.$$

(b) Interpretation and further calculation

$$\boxed{P_{A,\min}/P_0=R_p/2=0.010}.$$$$R_p>0,\ D<1\Rightarrow\boxed{\text{not exact Brewster incidence in the stated ideal model}}.$$

Physical check

A strongly polarized reflected beam need not be completely polarized. Combining total reflectance with polarization resolves both components.