# 1911 Encyclopædia Britannica/Mirage

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​MIRAGE (a French word, from mirer, to look at, se mirer, to be reflected), an optical illusion due to variations in the refractive index of the atmosphere. It embraces the phenomena of the visionary appearance of lakes in arid deserts, the images of ships and icebergs, frequently seen as if inverted and suspended in the atmosphere in the Polar Regions, the Fata Morgana, and “looming” as witnessed in mists or fogs.
In the article Refraction it is shown that a ray of light traversing a homogeneous medium is deviated from its rectilinear path when it enters a medium of different refractive index; it is therefore readily seen that the path of a ray through continuously varying media is necessarily curvilinear, being compounded of an infinite number of infinitesimally small rectilinear deviations. Our atmosphere is a medium of continuously varying refractive index. Meteorological optical phenomena, due to variations in the refractive index of the atmosphere, may be divided into groups: (1) those due to the permanent or normal variation experienced as one ascends in the atmosphere, and (2) those due to sporadic variations occasioned by irregular heating. The first variation must be taken into account in correcting geodetic observations of heights and astronomical observations of the heavenly bodies; it also has a considerable bearing on the phenomena of the twilight and the afterglow (see Refraction: § Astronomical; and Twilight). The second (or temperature) variation gives rise to phenomena which we proceed to discuss.
A common type of mirage is the appearance of an isolated lake frequently seen in hot sandy deserts, as in the Sahara, Turkestan, &c. The explanation is as follows: The sand, being abnormally heated by the solar rays, causes the neighbouring air to expand, consequently its density, and therefore its refractive index, is diminished, and attains a minimum value in the lowest layers. It increases as we ascend and reaches a maximum at a certain height, and then decreases according to the normal variation. Any object viewed across such an area is seen by two sets of rays: one set passing near the earth and assuming a curved path convex to the horizon, the second set more remote from the earth and concave to the horizon. The object thus appears double, an image being seen mirrored in the sand. The sky appears as a shining lake; mountains or palms may be similarly reflected, but it is to be noted that the
images are inverted (see fig.). Similar atmospheric conditions sometimes prevail in the air over large, bodies of water on cold autumn mornings. These phenomena have been experimentally realized by R. W. Wood (Phil. Mag., 1899, vol. xlvii.), who viewed objects over a series of heated slate slabs.
Another type of mirage, frequently observed at sea in the northern latitudes, is presented in the appearance of ships and icebergs as if inverted and suspended in the clouds. This is due to a stratum of hot air at some distance above the sea level, the rays of light near the horizon being practically horizontal, while those at greater elevations are fairly concave. It may happen that the change in density is so great that only the upper rays reach the eye; we are then met with the curious illusion of seeing inverted ships in the clouds, although nothing is visible on the ocean.
The Fata Morgana, frequently seen in the Straits of Messina, consists of an apparent vertical elongation of an object situated on the opposite shore. The distribution of density is similar to that attending a desert mirage, but the transition is not so abrupt. The object is really viewed through a horizontally stratified medium consisting of a central sheet of maximum refractive index, over- and under-laid by sheets of decreasing refractive power. The system consequently acts as a continuous lens, magnifying the object in a vertical direction.
If, in addition to this horizontal stratification, the atmosphere varies similarly in vertical planes, then the object would be magnified both horizontally and vertically. These conditions sometimes prevail in misty or foggy weather, more particularly at sea, and thus give rise to the phenomena known as “looming.” A famous example is the Brockengespenst or “spectre of the Brocken.” The chromatic halos which frequently encircle these images are due to diffraction. (See Corona.) It is interesting to note that lenses formed on non-homogeneous material, having the maximum refractive index along the central axis, have been prepared, and reproduce the effects caused by abnormal distribution of the density of the atmosphere.
The mathematical investigation of this subject was worked out by Gaspard Monge. For this aspect and further details, both descriptive and experimental, see J. Pernter, Meteorologische Optik (1906); E. Mascart, Traité d'optique (1899–1903); R. W. Wood, Physical Optics (1905); R. S. Heath, Geometrical Optics.