Optical Detection of Motion of an Object with a Refractive Index Coinciding with the Refractive Index of the Surroundings

Estimates of characteristics of light reflection from an object moving with a constant velocity in a medium whose refractive index coincides with the refractive index of the object are presented. The back-reflected radiation has a frequency shift owing to the Doppler effect, and the reflectivity turns out to be a quantity of the first order in the ratio of the velocity of motion to the velocity of light in a vacuum. If the velocity of motion of the surroundings near the object boundary varies in a boundary layer of a width that appreciably exceeds the wavelength, the reflectivity falls off exponentially with the ratio of these quantities. The estimates performed testify that the possibility of observing the effect of relativistic reflection under consideration is quite realistic.