As I have stated above, I cant do an extrapolation to higher wavelengths as the function is not a simple function for curve fitting. Mathematica that I have been using for the calculation is using a specific algorithm to do its calculations, but from my reading there are different forms of algorithm which will give slightly different answers (and have different accuracies). I have no idea which algorithm mathematica uses, nor can i vouch for its accuracy. If you want to be completely scientific, you have to bear in mind this fact of different computational methods, and the limitations of these methods.
What this means is that all the values calculated above (while self consistent as they use the same algorithm) may have different values.
Alas, I do not have enough knowledge in this area to know which algorithm to use in which circumstance, and I dont have the time to chase up on the different computational methods.
What i will say is this, from looking at the graphs of the index of air, I dont think there is a wavelength visible or not, that will give you exactly those angles and have a refractive index of ice of 1.2999. I cant say for sure that there is not, since there are many variables to consider in the calculation (not just angles and wavelength). Personally though, I think the match of red light of 700 nm of 1.2999 with the calculated value of 1.3069 is pretty good.
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