Image formation by an optically stratified medium: optics of mirage and looming

Abstract

An analytical theory of image formation in an optically stratified medium, with particular reference to the phenomena of mirage and looming, is presented; it is assumed that the variation of refractive index with height is exponential. The images in neither mirage nor looming are formed on the same vertical line as the object, a result contrary to popular notions. Some other interesting results are the prediction of a maximum as well as a minimum in the range of observation of mirage, the prediction of a maximum and minimum height of the object, for points outside which mirage is not seen, the prediction of a minimum in the range of observation of looming and finally the prediction of a maximum height of the object, for points above which looming is not observable. Some numerical calculations have also been made, and a physical discussion of the results is given.