I know that the speed of light, the universal constant of gravitation and the Planck's constant are considered to be the three fundamental constants of the universe. But, why is speed of light considered as a fundamental constant? The speed of light changes from medium to medium for satisfying Fermat's principle then, how can it be a constant?
Answer
But, why is speed of light considered as a fundamental constant?
c is an invariant speed; if something (not necessarily light) has speed c in one inertial reference frame (IRF), it has speed c in all IRFs.
This result follows from the Lorentz transformation which, empirically, gives the correct coordinate transformation between relatively moving IRFs.
Thus, c is a physical constant with units of speed. So it is c, the physical constant, that is constant.
Yes, light propagates with speed c in vacuum but there is nothing contradictory with light propagating with speed less than c in a medium. In other words, we do not denote the speed of light in a medium as c.
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