I'v been troubled by something. Einstein's second postulate determines the speed of light in empty space to be a constant c, measured by all observers to be the same. So I was thinking, it is possible to slow light by making it pass through a dense medium like water or glass. If we imagine such a medium in an absolute vacuum, with speed of light in the medium being c' < c, then what happens at the interface of the medium with the vacuum when a photon leaves the medium and enters the vacuum. According SR, the speed of light in a vacuum must always be measured as c. This means the velocity-time graph is discontinuous at this point which, to me at least, is unphysical. I mean, we're not talking about discrete orbits in a hydrogen atom here. Can someone explain this please?