Being that I have zero qualifications as an expert on C I will tell
you how I see it.. pun intended

First, C is specified as the speed of photon travel in a vacuum, per
definition... Or as our attorney brethern say it, Per Se...

Second, C' is the measured speed of the propagation of the wave front
we call light through an atomic medium, air, water, glass, diamond,
etc....

The thing to keep in mind is that the two, C and C', are not identical
physical entities...
C is the unimpeded propagation of a photon - i.e. a single entity -
through a non atomic medium we call a vacuum - 'aether' if you will...
The photon that left Proxima Centauri ~4 years ago is the same photon
that slams into the front lens of the Hubble telescope (according to
that photon's wrist watch that ~4 years happened instantaneously, but
that's another rant)...
Now if you were in orbit at the eyepiece of the Hubble the photon that
enters your retina is not the same Proxima Centauri photon that
slammed into the Hubble's mirror... And that makes all the
difference...

C' happens when the photon smashes into the Hubble's glass and is
caught up in the electrical fields sorrounding the atoms making up the
glass, primarily the electrical field of the outer (valence) electrons
of the Protons... Like a house fly at full speed hitting a spiders web
the photon begins to tumble and veer sideways and rapidly decellerate
causing it to dump it's energy, i.e. radiate an electromagnetic field
of it's own... The electron's field absorbs the energy radiated off
the photon, causing in increase in the electrons energy level, usually
forcing it to jump to a higher 'orbit'...

Now at this instant the photon has disappeared (eaten by the spider)
and the electron has been pumped up (like Hulk Hogan)... After a short
interval the electron drops back to a lower energy level emitting a
new photon... This photon takes off like a scalded rabbit at C (or
very near C) but doesn't get far before another electron field sucks
it up again... And so it goes for the passage of the photon (actually
information) through the atomic structure of the transparent
material... The photon that pops out of the eyepiece and slams into
your retina is the lebenty sebenth generation descendent of the
original photon that hit your scope... The process of repeated
absorption and emission of a photon by multiple electrons is what
slows the light (wave front) when it travels through transparent
material... (and also what creates refraction, circles of confusion,
and a bunch of other phenomena)

Clear as mud, eh wot...

denny / k8do