Hi,
I have an issue with the Fresnel amplitude coefficients. I know they are given in two versions, for spolarization and ppolarization. A version for unpolarized (randomly polarized) light is available for the power coefficients  it's just an average  but I could not find such an expression for the amplitude coefficients. From the power coefficient average expression I get:
$$r_\text{avg} = \sqrt{\frac{r_s^2 + r_p^2}{2}}$$
Which is obviously wrong, since this value is always real and positive which doesn't make sense for amplitude coefficients (I think).
So is there a simple expression for the average fractional amplitude of the reflected light assuming light is randomly polarized (equal amount of spolarized and ppolarized waves)? And can the result be extended to an arbitrary proportion of spolarized and ppolarized waves (say 25%, 30%, etc..)
Or does it simply not make sense to try and find an average of amplitudes? I need this to analyze interference effects, I could go with two versions dependent on the polarization of light, and average the final reflectance at the end, but it seems cleaner and easier to have a single expression. Thanks...
I should mention this is for a computer graphics project and I do not know that much about electromagnetism, please go easy on me :)
