As to how light "speeds back up" after leaving a substance, here is the easiest way of looking at it.
Photons always travel at c. When they enter a transparent substance, however, they encounter molecules/atoms. As they do so, the molecules absorb the photons. When that happens the photons cease to exist.
Then after a short delay, the molecule , re-emits a photon traveling in nearly the same direction as the first. This new photon, upon creation, begins to travel at c until it encounters another molecule.
These slight delays between absorption and emission, increases the time it take from the time a photon enters a substance to the time one emerges form the other side.
This give the impression that light slowed down while traveling through the subtance.
(If you knew that some friends had left their home, which was 60 miles distant from you, at a given time, and they arived at your house 1 1/2 hrs later, It would seem to you that they drove the distancea 40 mph. Even if, while on the road, they drove at 60 mph, but stopped for gas along the way, got a quick bite to eat somewhere, had to fix a flat , etc. )
Light travels though a substance in similar fits and starts.
RA What you say is true, but the actual computations and detailed theory are dificult. (Among the early contributors are some of the marques names in physics, Rayleigh (explained why the sky is blue), Einstein and Smolukowski who investigated and showed the importance of fluctuation in local numbers of molecular scatterers, less well known is Mie who developed the theory of why the rainbow looks as it does.
The slowdown occurs through interference inside the material -- the slowdown is reflected in the so-called group velocity of a wave packet , all frequencies treavel at c-- the scattering results in changes in the frequency of the light. The frequency shifts are due to, among other things, molecular recoil, and sometimes due to so-called radiative broadening due to the lifetimes of the excited molecular states.
But, once outside, the light suffers no interference, and so goes at c. There are no contradictions; the theory has been tested countless times -- including the theory of radar we all depend on while flying.
The theory, like most in physics, is descriptive, as are Maxwell's equations. We physicists make no pretension that we understand how, or why charges emit radiation or produce fields. But the modern world is testimony that once we assume fields, the resulting theory is staggeringly useful, and remarkably accurate.
Regards,
Reilly Atkinson
