Fizeau Experiment - Fresnel Drag Coefficient

Fresnel Drag Coefficient

Assume that water flows in the pipes at velocity v. According to the non-relativistic theory of the luminiferous aether, the speed of light should be increased when "dragged" along by the water, and decreased when "overcoming" the resistance of the water. The overall speed of a beam of light should be a simple additive sum of its speed through the water plus the speed of the water.

That is, if n is the index of refraction of water, so that c/n is the velocity of light in stationary water, then the predicted speed of light w in one arm would be

and the predicted speed in the other arm would be

Hence light traveling against the flow of water should be slower than light traveling with the flow of water.

The interference pattern between the two beams when the light is recombined at the observer depends upon the transit times over the two paths, and can be used to calculate the speed of light as a function of the speed of the water.

Fizeau found that

In other words, light appeared to be dragged by the water, but the magnitude of the dragging was much lower than expected.

The Fizeau experiment forced physicists to accept the empirical validity of an old, theoretically unsatisfactory theory of Augustin-Jean Fresnel (1818) that had been invoked to explain an 1810 experiment by Arago, namely, that a medium moving through the stationary aether drags light propagating through it with only a fraction of the medium's speed, with a dragging coefficient f given by

In 1895, Hendrik Lorentz predicted the existence of an extra term due to dispersion:

.