I thought that speed of the light in a medium can be slower that that in vacuum just because of the fact that it takes more time to be absorbed and re-emitted

I thought that speed of the light in a medium can be slower that that in vacuum just because of the fact that it takes more time to be absorbed and re-emitted by atoms, i.e. photons actually continue to travel at the same speed, but they are not the "same" photon.