Light refraction in the Earth’s atmosphere III. Inferior mirages: images locus

Our main goal is to find the locus of images formed as a result of an inferior mirage. To achieve our goal we show, at first, that, provided the beam entering a detection system has a small aperture, the image of a point object formed by that system in a vertical plane passing through the object is a point, regardless of whether the image formed by an optical system previously traversed by the beam has generated a non-point image of the object. Secondly, we show that the different images formed by the detection system, as its position relative to the object varies, are located on the caustic curve corresponding to the previously traversed optical system. Next, we have found the analytical expressions of the caustic curves corresponding to two particular cases, one of them being the inferior mirages. These expressions have been found by means of the Legendre antitransform of the asymptotic lines to the paths of light rays reaching the detector. For the case of inferior mirages, we have studied in detail the locus of the images in each vertical plane passing through the object as a function of the position of the object relative to the ground, its position relative to the detector, and the atmospheric conditions. Finally, we get somewhat into the matter of the images position as they would be seen by a casual observer of an inferior mirage.