The perfect demonstration of Snell’s Law doesn’t exi—pic.twitter.com/nv1KgASipt
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It also follows from the fact that light "takes the shortest path". Which is also related to Feynman's cancellation work.
Fermat's principle of least time is indeed an astounding fact, as Snell's law can be derived from that as well. I offered the Maxwell explanation since it seems the most well known/fundamental/comprehensible
Hahaha it's not a derivation.. c.f. Griffiths on Electromagnetic boundary conditions
or Huygens’ principle.
As Huygens' principle can be derived from Maxwell equations, the circle is closed 
I've read about a model of crawling soldiers going from mud to some water, and it gives something close but different to this, I don't know where I read that.
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