MIRAGE, an optical illusion due to progressive variations in the refractive indices of adjacent layers of the atmosphere. It embraces the phenomena of the visionary appearance of sheets of water in arid deserts, the images of ships and icebergs in the atmosphere of the Polar regions, the Fata Morgana, and "loom ing" as witnessed in mists or fogs.
A ray of light, when traversing a homogeneous medium is deviated from its original path by any transparent medium of different refractive index which it enters at an angle less than a right angle ; it is therefore readily seen that the path of a ray through continuously varying media is necessarily curved, being compounded of an infinite number of infinitesimally small rec tilinear deviations. The atmosphere is a medium of continuously varying refractive index. Meteorological optical phenomena, caused by variations in the refractive index of the atmosphere, may be grouped as: ( ) permanent variation as experienced dur ing a normal ascent through the atmosphere, and (2) sporadic variations occasioned by irregular heating. The first variation necessitates the correction of astronomical observations and of geodetic measurements of heights; it is also important in the phe nomena of the twilight (q.v.) and the afterglow. The second type of variation gives rise to mirages.
A common occurrence is the appearance of an isolated lake in hot sandy deserts. The sand, e.g., of the Sahara, being abnor mally heated by the sun, causes the neighbouring air to expand, and its density and refractive index, are diminished, the minimum value being attained in the lowest layers. It reaches a maximum at a certain height, and then decreases according to the permanent variation. Any object viewed across such a heated area is seen by two sets of rays : one set passing near the earth and assuming a path convex to the horizon, the second set more remote from the earth and concave to the horizon. The object will thus appear double for an inverted image is also seen as though mir rored by the sand. The sky's image appears as a sheet of water often surrounded by rocks, reeds and trees, all being reflections of actual objects but frequently distorted out of recognition. Similar
mirages may often be seen over smooth surfaces, e.g., tarred roads, on calm hot days, apparent pools of water flood the roadways and surrounding objects are reflected in them. For experimental veri fication of the phenomena see R. W. Wood, Phil. Mag. 1899.
A mirage, frequently observed at sea in high northern latitudes, is the appearance of ships and icebergs as if inverted and sus pended in the clouds. In this case, a stratum of hot air is at some distance above the sea level, the rays of light near the horizon are practically horizontal, while those at greater elevations are con cave. If the change in density is so great that only the upper rays reach the eye then inverted ships appear in the clouds, although nothing is visible on the ocean.
The Fata Morgana, of the Straits of Messina, consists of an apparent vertical elongation of an object situated on the opposite shore. The distribution of density resembles that attending a desert mirage, but the changes of refractive index are not so abrupt. The object is really viewed through horizontally stratified media consisting of a central sheet of maximum refractive index, over- and under-laid by sheets with decreasing refraction effects. The entire system acts as a lens, magnifying the object in a vertical direction. If, in addition to this type of horizontal stratification, the atmosphere possesses a similar vertical stratification, then the object would be magnified along two dimensions. These condi tions sometimes prevail in misty or foggy weather, more par ticularly at sea, and thus give rise to the phenomena known as "looming." A famous land example is the "spectre of the Brocken" (q.v.). The chromatic halos which so frequently encircle these appearances are caused by diffraction (see HALO). Lenses formed of non-homogeneous material and having the maximum refractive index along the central axis, have been prepared, and reproduce some of the effects already described.
The mathematical explanation of this subject was first given by Gaspard Monge; see J. Pernter, Meteorologische Optik (1906) ; E. Mascart, Traite d'optique (1899-1903) ; R. W. Wood, Physical Optics (1905) ; R. S. Heath, Geometrical Optics (1887).