Polarization by Reflection — Question 7

Question 7

A parallel Brewster window transmits p polarization through both faces

A lossless plate of index square root of three is surrounded by air. Light enters at its Brewster angle. The faces are parallel. Count only the directly transmitted beam; internally reflected secondary beams are excluded. Use the Brewster s reflectance $R_s=[(n^2-1)/(n^2+1)]^2$.

1. Show that the second face is also at its reverse Brewster angle and find direct p and s power transmission fractions.

2. For unpolarized input, find direct total transmission and degree of linear polarization.

Question 7 - Solution

A parallel Brewster window transmits p polarization through both faces

(a) Method and calculation

$$\theta_{B,\mathrm{in}}=60^\circ,\quad\theta_{\mathrm{inside}}=30^\circ=\tan^{-1}(1/n).$$$$R_s=1/4\Rightarrow\boxed{T_{p,\mathrm{direct}}=1,\quad T_{s,\mathrm{direct}}=(1-R_s)^2=9/16}.$$

(b) Interpretation and further calculation

$$\boxed{P_{\mathrm{direct}}/P_0=(1+9/16)/2=25/32}.$$$$\boxed{\mathcal P_{\mathrm{direct}}=\frac{1-9/16}{1+9/16}=7/25=0.28}.$$

Physical check

The reverse Brewster angle matches the internal angle at the second parallel face. The s result here deliberately excludes later emerging beams.