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History of refraction begins with Ptolemy, at least this is the earliest source that survived). He apparently understood that altitudes of celestial bodies are affected by refraction, though we do not find this in his Almagest. He deals with refraction in his Optics (and this is "physical refraction" rather than "astronomical refraction", for long time these things were treated separately.

In his Optics, Ptolemy describes an experiment with a water vessel whose purpose is to determine the law of refraction. This is a very rare instance that a physical experiment is described by an ancient author. Almost unique such case. However, analysis of his numerical data suggests that the experiment was not really performed. His data fit a parabola rather than a sinusoid which a real experiment would give. So apparently his experiment was written only to demonstrate his (incorrect) theory by a numerical example.

This shows that the ancients at least tried to discover the law of refraction, though they did not succeed (unlike the law of reflection which they discovered and used the correct law).

The true law of refraction (in the simplest case of a ray passing the surface of separation of two media) was discovered by Willebrord Snell, a Dutch scientist in 17th century. But atmospheric refraction is much more difficult since the rays of various angles pass through different layers of the air, and the refrangibility of the air changes with height. The correct law was mathematically derived only in the beginning of 19th century, and it is explained in great detail in the great book of Chauvenet on Astronomical instruments.

Alex.