This is quite nuanced and not as most people assume.

It is the "phase velocity of light in that medium" that is exceeded.

phase velocity of light in a medium = speed of light / refractive index of the medium.

Thus the EM wave is slowed down in a medium and so a charged particle can exceed it producing Cherenkov radiation. This is similar to a sonic boom in atmosphere when speed of sound is exceeded. In both cases the object is traveling faster than the wavefront.

It is only in vacuum that "phase velocity of light" = "group velocity of light" = c (i.e. 300,000 km/sec)

What really is the speed of light in a medium/vacuum, group or phase velocity? - https://physics.stackexchange.com/questions/450377/what-real...