No, Galileo was the first to try to determine the speed of light, which he did never succe on doing. Ole Rømer (Ole Roemer or Olaus Christensen Roemer) was the first to measure the speed of light. Even though it is not as precise as it is today. We then later had Maxwell that found it by using formulars. Which he found odd, since he was studying electromagnetic waves.
Then we had the whole aether problem. Cause if it was a wave, then what would it travel in. Here the Michelson–Morley experiment comes in.
Which is rather famouse today, not that they ever succed. Then later we had Einstein who killed the Aether.
Today we believe it to be a constant. I am not stating that it is, but every experiment seems to point the way.
Here is some good reading of how to measure the speed of light;
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html
We believe so firmly on that the speed of light is a constant and that it is the natural speed limit. So when CERN data showed they found a particle that moved faster. Then they delayed the release to try to figure out the error. Which they could not find out. So they published it, and physicst came to CERN and found it was a error two articles about it here;
https://www.telegraph.co.uk/news/science/8782895/CERN-scientists-break-the-speed-of-light.html
https://www.telegraph.co.uk/news/science/science-news/9100009/Scientists-did-not-break-speed-of-light-it-was-a-faulty-wire.html
Now if you are considering a prisme for instance. That the light "bend" (light does not bend) which it does not, then form a rainbow. Then you have to consider what it meant with light. Is it the light beam or the photon?. We would acctually have most of modern physics breaks down, if it was proven that Theory of relativity was incorrect. We even use quantum mechanics relativistcly which would break down if not the speed of light where a constant.
Notice when I write "c" I do not talk about the speed of light in a medium. However, I talk about the speed of light in vacuum. Where it is in fact a constant. Then it becomes another constant in air for instance. Which is almost the same as the speed in vacuum.
We do experimental test to show that the formulars/theory holds not the other way around.
Regards
Sorry for the long comment (:
