Answer: no, it is not observed. This is because the natural (and, incidentally, the only) satellite of our planet does not have a dense enough atmosphere for this effect to manifest itself. Let me remind you what refraction is. It is customary to understand it as a change in the direction of a ray that occurs at the border of two media (it can also be one medium). With this phenomenon, the speed of propagation of the ox (ray) is not the same.
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