Why is the square of the speed of light equal to the reciprocal of the permeability times the dielectric constant
Light is an electromagnetic wave, that is, a changing electric field produces a changing magnetic field, which in turn produces a changing electric field, from which light spreads
The exact solutions of these two fields are obtained from Maxwell's equations, and finally a wave equation is obtained. One conclusion of the wave equation is that the square of the speed of light is equal to the permeability times the dielectric constant