Classical Electrodynamics · Problem 11.8

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · fizeau-experiment-relativistic

Problem

(a) Use the relativistic velocity addition law and the invariance of phase to discuss the Fizeau experiments on the velocity of propagation of light in moving liquids. Show that for liquid flow at a speed

v

parallel or antiparallel to the path of the light the speed of the light, as observed in the laboratory, is given to first order in

v

u = \frac{c}{n(\omega)} \pm v\left(1 - \frac{1}{n^2} + \frac{\omega}{n}\frac{dn(\omega)}{d\omega}\right)

where

\omega

is the frequency of the light in the laboratory (in the liquid and outside it) and

n(\omega)

is the index of refraction of the liquid. Because of the extinction theorem, it is assumed that the light travels with speed

u' = c/n(\omega')

relative to the moving liquid. (b) Consult the paper of W. M. Macek, J. R. Schneider, and R. M. Salamon [J. Appl. Phys. 35, 2556 (1964)] and discuss the status of the Fizeau experiments.

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