Optical air mass and refraction in a Rayleigh atmosphere

Analytical expressions for the spectral optical air mass m and the angle of refraction omega in a molecular Rayleigh atmosphere were found in dependence on the air density profile. The correlation between m and omega is discussed. The theoretical expressions obtained in this paper show that both the optical air mass and the refraction angle close to the horizon depend critically on the vertical profile of the air density and may vary over a wide range (approx 35-43 arcmin for m and approx 31-44 arcmin for omega at the Earth's surface). This fact implies that the formulae independent of any meteorological parameter cannot express the optical air mass or the refraction angle with a sufficient accuracy. Therefore, comparing such formulae on the base of their accuracy has no sense.