When a photon enters a medium, the fact that it’s an electromagnetic wave becomes crucial.
There’s a complex back-and-forth interaction between the photon and the charges in the medium (primarily electrons), where the photon makes them wiggle, and that wiggling in turn makes waves in the electromagnetic field that interact with the photon.
The result of that is that the wave that travels through the medium isn’t quite the same photon that entered, but once it leaves all that interaction stops and it’s the old photon again, because none of those interactions can actually permanently change the photon.
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