Properties of optical ducts, their chromatism and its effects on astronomical refraction

The fundamental quadrature governing light rays in a spherically symmetrical medium is first recalled. A rigorous discussion of some qualitative properties of its solutions follows, using the Young-Kattawar diagram which leads to a geometric formulation of the ray curvature. The case of an optical duct is deepened, analyzing transfer curves for different positions of the observer with respect to the duct. New analytical expressions for their wavelength dependence are derived, and their numerical consequences are coherent with computer simulations.