Obtaining the relativistic formula for the refraction of light and the practice of its application

the calculation of the refractive indices of light, new relativistic formula, new relativistic formula for the refraction of light Abstract. The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.


Abstract.
The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.
Keywords. Relativistic dispersion formula, new dispersion formula, empirical dispersion formulas, a formula for determining the total energy of a moving body, the energy density index of electron clouds, the calculation of the refractive indices of light.

Introduction.
Currently, there are no physical formulas that can be applied to a wide range of transparent substances. For example, the well-known physical formula of Lorentz-Lorentz, which is based on the dependence of the refractive index of light on the density of a substance, is valid only for isotropic media (gases, non-polar liquids, cubic crystals) and is not applicable for most transparent substances. Therefore, in practice, to calculate the refractive indices, empirical dispersion formulas (Cauchy, Hartmann, etc.) are used. These formulas are quite accurate, but at the same time they are not physical formulas.

Methods.
Let's start with the well-known formula, where the refractive index of light in a transparent substance is = ⁄ , where is the speed of light in vacuum, is the speed of light in matter.
In this work, it is hypothesized that the speed of propagation of photons in a transparent substance depends on the energy of electron clouds of atoms of the substance: the higher the density of the electron clouds, the lower the speed of the photons and vice versa. In this case, the greater the energy of the photons entering the substance, the more the electron clouds of the atoms of the substance are "condensed" by this energy. As a result of this circumstance, electromagnetic waves with different wavelengths propagate in the same transparent substance at different speeds. Thus, there is an inverse relationship between the energy density of electron clouds of atoms of matter and the speed of propagation of photons in matter. To determine this dependence and then obtain the dispersion formula, we use in this study the relativistic Einstein formula to determine the total energy of a moving body: Where is the total energy of a moving body.
− energy of a body at rest.
is the speed of the body.
Let's transform the formula (1-1) and as a result we get: Where is an indicator of the ratio of the energy of a body at rest to the total energy of a moving body, < < 1.
Now we apply formula (1-2) to the speed of propagation of photons in a transparent substance: Where γ is the speed of propagation of photons in the electron clouds of atoms of a transparent substance.
is a dimensionless indicator of the energy density of electron clouds of a transparent substance, < < 1.
Let's transform the formula (1-3) and get: Where is the refractive index of light in the substance ( = ⁄ ).
Let's reveal the value of in the formula (1-4): Where is a dimensionless basic indicator of the energy density of electron clouds of a transparent substance. (1-6) Where is the coefficient of proportionality, J −1 .
Replace with a single coefficient and obtain a new dispersion formula: Where is the coefficient of proportionality, nm.
The coefficient is individual for each substance and depends on the To be able to verify with the table data, they will be sent to the editor in a separate file). The first column of the table contains the basic indicators The same method was applied to the rest of the indicators in other substances. The author believes that this approach is the most correct, because the known laboratory parameters, after being obtained experimentally, were also rounded to a certain sign. From this it follows that when comparing the refractive indices, the equality of the commas after zero must be observed, because otherwise, the calculation accuracy indices may increase unreasonably or, conversely, decrease.
After rounding off the calculated indices, they were compared with laboratory refractive indices and the discrepancy between them was determined.
The results were tabulated.
Results and discussion. Table 1 shows the 26 calculated refractive indices of light in 5 transparent substances, which were calculated using the new physical formula.
Comparison of the indicators calculated by the new dispersion formula with laboratory indicators showed the following: in an inert gas the discrepancy was 10 -7 , in water and solids ±10 -6 − 10 -5 . In this case, the calculated range was more than 100 nm.