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Fermat's principle doesn't explain anything. It is a valid
model for the propagation of light, that's all. Physics
doesn't explain; it can only describe. It is a good idea to
keep this fact always in the front of your mind. Not doing so
is the cognitive error which makes the religious believe they
have all the answers.
The rays always choose the path which minimizes this transit
time. This analogous as to why a cross country auto traveler takes the
bypass (rather than going straight through downtown) around a city which is
between the traveller's point of departure and destination when the
traveller approaches the city during rush hour.
David Bowman