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When I asked why did light follow the law of reflection, I was answered that it obeys the principle of least time. So my question is, why does it even obey the principle of least time?

Qmechanic
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    I suggest you research Huygens-Fresnel principle of wave optics. Using this explanation, it is easy to geometrically deduce why light bends the way it does. – Obliv Nov 13 '16 at 05:05
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    You may be interested in this: http://www.feynmanlectures.caltech.edu/I_26.html#Ch26-S6 , where Feynman explains "what actually happens, how the whole thing really works, from what we now believe is the correct, quantum-dynamically accurate viewpoint". – Simon Nov 13 '16 at 05:11
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    I give a fairly thorough derivation of Fermat's principle from Maxwell's equations here: http://physics.stackexchange.com/a/151488/26076. Some short comments also show that the notion is more general than Maxwell's equations and applied, for example, to sound and other waves governed by D'Alembert's wave equation: http://physics.stackexchange.com/a/203507/26076 – Selene Routley Nov 13 '16 at 08:37
  • Related: http://physics.stackexchange.com/q/2041/2451 , http://physics.stackexchange.com/q/82737/2451 and links therein. – Qmechanic Nov 13 '16 at 11:54
  • Related: https://physics.stackexchange.com/q/375170/ – Gavin R. Putland Aug 10 '18 at 07:56

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Summarizing some of the comments as an answer:

There are some excellent reference in the comments such as

Feynman's lectures: http://www.feynmanlectures.caltech.edu/I_26.html#Ch26-S6

and Fermat's principle from Maxwell's equations: https://physics.stackexchange.com/a/151488/26076

and also how Snell's law follows from the principle of least time: https://physics.stackexchange.com/a/151488/26076

The question you are asking is quite wide as it allows for answers of the type 'A' follows from 'B'. However at some point we come the the point that 'B' follows from 'C' and 'C' is just the way that nature behaves.