It must be noticed that the observation of Doppler effect by a prism depends entirely on dispersion; i.e. on waves of different length being affected differently. But prisms can be constructed whose dispersion is corrected and neutralised. Such achromatic prisms, if perfectly achromatic, will treat waves of all sizes alike; and, accordingly, the shortening of the waves from a moving source will not produce any effect. Achromatic prisms will therefore behave to terrestrial and to extra-terrestrial sources, i.e. to relatively stationary and relatively moving sources, in the same way.
This must be recollected in connexion with several of the negative results rightly obtained by some observers; such as Arago, for instance, who applied an achromatic prism to a star which the earth was approaching, without observing any effect. A Doppler effect should have been observed by a dispersive prism, but not by an achromatic one: for the refractive index of a substance is not affected by any motion of the earth.
It is not reasonable to expect that refractive index would be affected, since it depends in simple geometrical fashion on retarded velocity, i.e. on optical etherial loading or apparent extra internal density.
An achromatic grating, however, is (rashly speaking) an impossibility.
Effect of Transparent Matter.
But when a ray is travelling through transparent matter, will not motion of that matter affect its course?
If the matter is moved relatively to source and receiver, as in Fizeau's experiment with running water, most certainly it will; to the full effect of the loading or extra or travelling density, (μ²-1), compared with the total density μ².
This fraction of the velocity of the material medium must directly influence the velocity of light, for the waves will be conveyed in the sense of the material motion u, with the additional speed u(μ²-1) / μ². (See also Appendix [3].)
But if the transparent matter through which the light is going is stationary with respect to source and receiver—only sharing with them the general planetary motion, i.e. being subject to the opposite all-pervading ether drift,—then no influence due to the drift can be experienced; for the free ether of space behaves just as it would if the matter were not there. This can be shown more elaborately by the following calculation.
Optical Effect of Ether Drift through Dense
Stationary Bodies.