OK, well I'm just working through some optics stuff I've got to do...

 

And I've got to substitute into the Fresnel equations, for [math]\theta_1[/math] where the 1 is for transmitted and 0 is for incident/reflected.

 

So here goes...

 

snell's law: [math]n_1 \sin\theta_1 = n_0 \sin\theta_0[/math]

square it:

 

[math]n_1^2 \sin^2\theta_1 = n_0^2 \sin^2\theta_0[/math]

 

subs in: [math]sin^2\theta_1=1-cos^2\theta_1[/math]

 

=> [math]n_0^2 \sin^2\theta_0 = n_1^2 (1-cos^2\theta_1)[/math]

 

=> [math]\frac {\sqrt {n_1^2-n_0^2 \sin^2\theta_0}} {n_1} =cos\theta_1[/math]

 

 

Now that's all well and good, but n₁ = n+ik, so which of these is true:

 

[math]n_1^2 = \sqrt{n^2 + k^2}[/math]

 

OR

 

[math]n_1^2 = n^2 + (ki)^2+ink[/math]

 

This then has to be substituted into:

 

[math]r_{pp} = \frac {n1\cos\theta_0 - n0\cos\theta_1} {n1\cos\theta_0 + n0\cos\theta_1}[/math]

 

And then R = r_ppr*_pp

http://www.baylee-online.net/Projects/Raytracing/Algorithms/LawsOfOptic