LIGHT ABERRATION IN OPTICAL ANISOTROPIC SINGLE-AXIS MEDIUM

The entrainment of the light flux by a uniaxial anisotropic medium and its influence on the measurement of stellar aberration are analyzed. The influence of the entrainment of the light flux by an isotropic medium on the measurement of stellar aberration was considered by Fresnel early. The absence of such influence was confirmed by Erie's experience when filling the telescope tube with water. The formula itself was perfectly confirmed by Fizeau's experiments with moving water and the repetition of this experiment with an increase in the accuracy of measurements by Michelson, Zeeman, and others. G.A. Lorentz already on the basis of the electromagnetic theory specified the formula with allowance for the frequency dispersion of the light flux. A. Einstein made an analysis of the schemes of experiments for determining the drag coefficient, covering all possible variants of similar experiments. As a result, he obtained Fresnel and Lorentz formulas, taking into account the frequency dispersion of light, starting from the theory of relativity. The entrainment of light and its influence on the measurement of stellar aberration by a uniaxial anisotropic medium have not been considered anywhere. An analysis of such influence is carried out. The results of the analysis indicate the possibility of measuring the current value of stellar aberration using a uniaxial anisotropic medium. The concept of active light aberration is introduced. The proposed schemes of experiments of using the entrainment of a light flux by an anisotropic substance for measuring the current value of stellar aberration are investigated. It is concluded that it is possible to study the determination of the current velocity of an inertial system relative to the light flux.

Let us analyze the influence of light carrying away by single-axis anisotropic medium on measurement of star aberration.
In 1818, Fresnel proposed theory of partial light flux carrying away by a moving substance having carrying away coefficient Based on the simplest mechanical model on full carrying away of thee the part by bodies (the part which forms its over-density as compared with the surrounding ether) he obtained correct formula [1,2] confirmed by experiments. This formula was excellently proved by Fizeau experiment (1851) with moving water, repeated by Michelson (1886) and Zeeman (1914) with increase of measurement accuracy.
Base done lector magnetic theory G.A. Lorentz (1886) corrected the formula with the account of light flux frequency dispersion [3]. Zeeman experiments with moving rods confirmed the existence of Lorentz dispersion term.
А. Einstein highly appreciated the significance of Fizeau experiment. «The answer to this problem is given by highly important experiment made more than half a century ago by brilliant physicist Fizeau…».
«Although its hold be noted that long before appearance of relativity theory G.A. Lorentz explained the theory of this phenomenon and justified it by purely electrodynamics method by means of certain hypothesis about electromagnetic matter structure.
However this does not diminish the evidential force of Fizeau experiment has experiment um cruces in favors of relativity theory, since Maxwell-Lorentz electrodynamics which was used as original theory do not contradict the relativity theory». «Fizeau experiment is fundamental also for the special relativity theory» [4].
A. Einstein made anal by sis based on relativity theory of three scheme variants of experiments on determination of carrying away coefficient embracing all possible variants of similar experiments. As a result, he obtained Fresnel and Lorentz formulae with the account of light frequency dispersion. This once again proved correctness oft here relativity theory [4].
W.E. Frankfurt, A.M. Frank [5] note that «in the relativity theory results of these experiments are explained simply as consequence of relativity velocity addition formula ' 1 Taking only terms of the first order, we obtain (where ' c is the speed of light with respect to the fixed installation and the observer).
. Although the formula has the same appearance here "partial carrying away" is the result of pure metric properties and is not connected with any assumption about substance structure or ether properties» [5].
A. Somerfield [6] investigated aberration and crystal optics based on Lorentz transformations however all these investigations and experiments related to longitudinal, as to direction of propagation, light flux carrying away but transverse carrying away was not considered.
At the same time (1818), Fresnel investigated the influence of such transverse carrying away on star aberration measuring. He considered the experiment with filling a telescope tube with water and made the conclusion about absence of influence of such filling on the value of star aberration. «Although this experiment was not yet made, but I have no doubt, that it will support this conclusion …» he wrote to Arago in 1818.
Eri made such an experiment in 1871, which confirmed permanency of star aberration angle. The analysis of such filling in was made in detail in [7].
In 1977 H. Bilger and W. Stawell conducted the experiment, wherein light propagated in the rotating optical disc of the annular laser interferometer. [8] Anisotropy of the electromagnetic radiation velocity space under transversal light entrainment in the rotating optical disc was investigated by V.O. Gladyshev, P.S. Tiunov, A.D. Leontiev, T.M. Gladysheva, E.A. Sharandin. By anisotropy in this case we mean the dependence of the propagation velocity of light in the optical medium on the velocity and direction of motion of the medium [9] All this investigations are related to the light propagation in the isotropic mediums.
The main purpose of this work is to study the effect of the partial entrainment of a light flux by an optically anisotropic uniaxial substance on the measurement of stellar aberration.

THE TRANSVERSE ENTRAINMENT OF THE LIGHT FLUX BY AN ANISOTROPIC SUBSTANCE
Examine consider influence of the partial light flux carrying away by the anisotropic substance on the star aberration with different refraction indices along telescope axis and in transverse direction for an extraordinary beam.
Assume a star S be observed through an unfilled telescope (Fig. 1). Due to star aberration because of telescope motion at speed V , its axis is directed towards 1 0 O S at the angle n is the refraction index in the direction of speed V . This is equivalent to the decrease of speed V by the value V with coefficient Speed n V , with the account of carrying away will become α we will obtain the value of the new aberration angle α .
For is anisotropic substances 1 k = and 0 α α = , but for anisotropic substances 1 k ≠ and e α differs from 0 α .

STUDY OF THE SCHEMES OF EXPERIMENTS USING AN ANISOTROPIC SUBSTANCE TO MEASURE THE CURRENT ABERRATION VALUE
Hence we will determine the aberration angle α 0 of the star S 3. Let us install a single-axis doubly refracting crystal 1, with crystal faces being perpendicular to its optical axis, so that optical axis of the crystal was parallel to the telescopic axis 4 (Fig. 3). We'll observe the star through the telescope aligning the star image by means of the ordinary light beam with telescope cross sight reticule 6. The star light flux will fall on the crystal face at the aberration angle α 0 . In the crystal the light flux will divide into ordinary and extraordinary flows having different direction of the linear polarization. Due to different refract ion indices e o n n ≠ , they will get refracted at different refraction angles. , so e r depends upon the direction with respect to the optical axis and upon the value of the crystal motion speed (Fig. 1,2).
The main influence on the extraordinary light beam refraction angle at small e r will be exerted by the extraordinary light beam carrying away during crystal motion perpendicular to the optical axis in the angle e r plane where the difference o e n n − is maximum, i.e., the difference between angles of propagation of the ordinary and extraordinary light beams will be determined in this case by the lateral speed of the telescope motion (Fig.3).
If to take into account ( ( ) ) where c -is the speed of the ordinary light beam in the crystal, t -time of passing of the ordinary light beam along the crystal axis.
On the other hand Thus, observing the star through the telescope with a single-axis doubly refracting crystal, align the star image by means of ordinary light beams with the cross sight reticule and measure the distance 2 O e between star images by the ordinary and extraordinary light beams. Knowing n 0 , n e and crystal length 1 2 O O we determine 0 α , without changing the direction of the observer's motion. The aberration direction is determined by the direction of the star image shifting by extraordinary light beams in the focal plane of the telescope.
Lorentze transformation defined movement effect (second-order quantities t , r proportional to