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Understanding atmospheric refraction, particularly of ultraviolet, and into the blue part of the visible spectrum is of great interest to me. Although, I have a strong background in trigonometry and geometry, I am very much interested in how these are applied in the context mentioned.

Are there any references (books, papers and the like), that are mathematically rigourous, but also have examples of how the mathematics is applied to atmospheric refraction? Are there any other mathematical knowledge that would be required?

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I cannot exactly suggest any sources, but a simple study of refraction is profited by Fermat's least time principle –  Torsten Hĕrculĕ Cärlemän Jan 8 at 12:21
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Google "Rayleigh Scattering" as well. A lot of atmospheric phenomena are particle-related, not just Snell-ish dispersion. –  Carl Witthoft Jan 8 at 12:48
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