How confident can we be that the speed of light in a medium is constant? I have recently found this article http://news.harvard.edu/gazette/1999/02.18/light.html it tells that physicists have been able to slow the speed of light. Is this hokum? If not how is it possible to use light as a measure of distance? Surely doing this would effect the waveform of light rendering it impossible to tell how far it has travelled or how long it has been travelling.
 A: That article is about slowing the speed of light in a physical medium (note the mention of the 'exotic medium' in the third paragraph), a common and well-known phenomenon (even ordinary transparent mediums like water or glass will slow light waves traveling through them to some extent), the newsworthy aspect was just the huge degree of slowing they were able to achieve. From what I understand, in quantum theory that basic explanation is that the photons are being repeatedly absorbed and re-emitted as they travel through the medium (not by individual particles of the medium but rather by collective vibrational modes known as 'phonons', see the discussion here), which slows them down even though they still travel at the speed of c between absorptions.
A: Actually The velocity of light in a Vacuum is now used to define the 
length of one meter.
Yes the velocity of light in different mediums is different, and when
light passes from one medium to another, its velocity changes.
At the interface, there is both reflection and refraction of light,
and a change in velocity, however slight.
This is why light is specified as a velocity " in a vacuum "
If I remember right V = 299, 792, 458 meters per second " in a vacuum "
The 1925 Michelson Experiment came up with a slightly lower number, but
his experiment was from mountain top to mountain top in California thru
a smoke filled valley air.  The light needed to make 4224 complete
round trips across the valley and back to the source every second to
synchronize with a spinning glass mirror that had 16 facettes on a circle.
This means the one way distance in a vacuum would need to be 
299,792,458 / 8448 = 35,486.79664 meters of travel distance apart.
if the light had traveled in a vacuum.
The actual distance was less, so the velocity of light in smoky air
was less. I will look up my answer to this distance.
Michelson did have a slight error in his calculated distance because
for the thing to work the distance and the RPM's of the machine needed
to both be exact numbers.
I looked up my calculations for the actual distances traveled by the
light and found the following.
Actual one way distance was 35,424.42968 meters x 8448 = 299,265,581.9 m/sec
in smoky atmosphere.  This is 99.824253% of the speed of light in
a Vacuum.
If you look up Michelson's 1925 experiment on the web, you will see that 
he made a tiny distance error in the last 10 cm of the internal set up
of his contraption.
I had thought this method could be utilized to measure atmospheric
density between two points. If the atmospheric density changes, then the 
light velocity will change, and the cyclical resonance distance will change.
A: There are two things usually called, the speed of light.  
The first thing $c=\sqrt{\frac{1}{\epsilon_0\mu_0}}$, a number that is related to the electromagnetic properties of the classical vacuum, so you can measure $\epsilon_0$ by doing electric measurements, and measure $\mu_0$ by doing magnetic measurements, and then compute $c$ from those experimental results.
Since any inertial frame could do those same measurements, they would compute the same $c=\sqrt{\frac{1}{\epsilon_0\mu_0}}$, so the number $c$ doesn't change. But it also turns out that electromagnetic waves (e.g. light) can travel through the classical vacuum, and they travel at speed $c$, so we call it the speed of light (in a vacuum).  Since every inertial frame also sees the same laws, every inertial frame sees the same fact that electromagnetic waves (e.g. light) can travel through the classical vacuum, and they travel at speed $c$.  (Also the speed $c$ of the wave is not related to the speed of the source.) These facts are all sometimes what is meant by the speed of light (in a vacuum) is constant.  That $c$ doesn't depend on your inertial frame, that the speed of the wave doesn't depend on the source, and that the speed of the wave doesn't depend on the inertial frame.  OK, so the speed $c$ doesn't ever change, but it is not the speed of light, it is only the speed of light in a vacuum.
So, the second thing that is often called the speed of light, is the speed of an electromagnetic wave in a medium (air, glass, water, something exotic, etc.). This is not constant, if fact there are frames (relative to the medium) where the speed of an electromagnetic wave in that medium is zero.
A: I wanted to make this a comment, but I don't have enough points yet. I remember studying this back in the 2nd semester of E&M (relativistic) and like most things in physics, it's hard to explain what's really going on in English. 
The model we used to explain the "slowing" of light in a medium was to model each of the atoms as a harmonic oscillator (like a spring attached to fixed point) and when the light - previously traveling in a vacuum - hit the medium, it turned from pure vacuum vibrations into springy electromagnetic atom vibrations. "Plasmons" i think is the correct name for these. If the medium is opaque to the incident light's wavelength, surface plasmons are generated.  
