In the Fizeau experiment light travels at c/n (in the refractive index of water) when the water doesnt move through the experimental setup . But when the water flows at v through the setup towards the light source, as Fizeau did, the light travels at a slower speed through the pipe. But not by as much as if one subtracted the v of the water from c/n in water. This means that if you were to move with the water during the experiment (or better, you and the tube of water dont move and the light source does) then that means that the light is no longer moving through the water at c in the refractive index of water . And instead it is moving slightly faster or slower through the water then c in water would normally give. Depending on the direction of the flow of the water relative to the source. The irony of this is that, although Einstein apparently said this effect was an important consideration in devising SR. It also is true, that the Fizeau effect is proof that the speed of light in water can be c+-v, if the source moves relative to the observor. Contradicting the prediction of SR that light is always travelling at c for that medium.
The speed of light defined by the usual (Fizeau formula) is..
c/n +-v(1-1/n^2),..where (1-1/n^2) =0.4347
This accurately predicts the observations.
In effect what is happening is that in the same amount of time t, as when the water doesn’t flow, more water has to be travelled through by the lightbeam as it travels from source to detector. This means that the water becomes more dense as a refractive medium. So a classical calculation should reflect this by multiplying the refractive index by the refractive index to find out how the added v of the water affects the light speed.
Aside from Fizeau’s original formula, cited above, there are various other fairly straightforward ways to calculate the observed speed differences in Fizeau that I have formulated. Including:
c/n+-v{n^2-n}
where {n^2-n} = 0.4389
Or: c/n+-v[{(n-1)+(n-1)}^2]
Or: c/n+-(V x (1-(n-1)/n)
(c/n+-(V x .67))/n
