Formation of Mirages in the Atmosphere
Formation of Mirages in the Atmosphere
Kocharyan Vilen
Summary
Key words: refraction, variable refractive index, Fermat’s principle, Euler’s relation, equation of the light ray trajectory, parabolic trajectory
The paper demonstrates that in the Earth’s troposphere, where air particles are largely uncharged and the atmosphere behaves as a dielectric with negligible absorption and a refractive index close to unity, the dependence of the refractive index of air on altitude can be approximated by a linear function. An equation is derived for the trajectories of light rays in a medium with a variable refractive index. The solution to this equation shows that in an atmosphere with a linearly varying refractive index, light rays are continuously refracted and propagate along parabolic trajectories, resulting in atmospheric refraction and optical mirages. When the refractive index of air decreases with altitude, objects located at a large distance from the observer appear elevated (sometimes inverted) above the Earth’s surface (superior mirages). When the refractive index increases with altitude (as is often the case in deserts), objects appear to be located on the Earth’s surface (inferior mirages).