B. The Fizeau's experiment (also Michelson)---[ Return home ]

The experiment has been performed by Fizeau in 1859 and in a better way by Michelson and Morley in 1886.

M.H. Fizeau, Ann. de Chim. et de Phys., 3e série, T. LVII, (décember 1859), pp. 385-404.

A.A. Morley and E.W. Morley, AM. Jour. Sci., Third Series, Vol. XXXI, no. 185, (1886), pp. 377-386.

A simplified setup of the experiment is represented on the figure below.

The results of Michelson-Morley with L= 6.151 m is that when the water is in motion at the velocity of 7.65 m/s a fringe displacement converted in time of 1.63 E(-15) seconds occurs. But with a velocity of 5.67 m/s, the phase shift is of 1.198 E(-15) seconds.

We are going to see here if such a result is compatible with the dispersion formula obtained in the Hoek's experiment and if it is due to the classical Doppler effect.

When the light beam of frequency Fo is in the direction of the motion of the water, the formula to use is: . But as the medium must be considered in motion the frequency Fo in the formula, must be replaced by Fo.[(c-v)/c] due to the classical Doppler effect.

The same way, when the light beam is not the direction of the motion of the water, the frequency Fo must be replaced by Fo.[(c+v)/c] in the following formula:

.

Now,as it is clear that the time delay in the direction of motion of the water is:

T+=[(L/w+)+(L/w+)] and in the opposite direction: T-=[(L/w-)+(L/w-)], the expected phase shift is T=(T+)-(T-)=2L[(1/w+)-(1/w-)].

Thus, with a computer program we have adjusted the parameter d=4.318E(-7)m in order to obtain the phase shift of T=1.198E(-15) second with v= 5.67 m/s and with

Fo= 5.2595E(+14)Hz the frequency used by Michelson.

Like that we obtain an index c/w- = c/w+ of 1.33 which is exact for the water at this frequency.

More, when the velocity is v=7.65 m/s, the time phase shift calculated is: 1.61E(-15) seconds in full agreement with the other experimental result of 1.63E(-15)seconds.

Thus, we have good reasons to believe like in the Hoek's experiment that water behaves like a rectangular waveguide of distance between the walls of 4.318E(-7)m, but obviously if the frequency changes weakly (it is the case here due to the weak Doppler effect).

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