Mirage (Fr., from Lat. mirari, to wonder), an appearance of distant objects in the air, as if standing in the sky, or reflected from the surface of water. It is produced by refraction in strata of different densities, decreasing or increasing rapidly, and sometimes by refraction and reflection combined. The appearances are those which have received the general name of unusual refraction. The phenomena of mirage are said to have been first explained by Monge, while accompanying Bonaparte's Egyptian expedition. There are several cases, of which the four following are the most common: 1, the mirage of the desert, which has the appearance of inverted objects, or reflections from the surface of water; 2, that which has the appearance of objects inverted in the air, and which is seen over the surface of water; 3, simple looming, when objects appear to be elevated above their real level, but are not inverted, the appearance usually taking place over the surface of water; 4, a combination of the two preceding, in which there are appearances of objects both erect and inverted. The causes, in many instances, are not easy to assign definitely. The mirage of the desert and the appearance of an inverted image of an object over the surface of water are usually explained as follows.

In the first case the aerial strata decrease in density from above downward, in consequence of the cooling of the upper strata from radiation, and the warming of the lower by the hot sand. Let fig. 1, in which the curves are exaggerated, serve for explanation. By referring to the article Light it will be seen that in refraction there is a certain angle at which a ray of light, having passed through one medium, on coming to the surface will not pass out of the medium into the next and suffer refraction, but will be totally reflected back into the first medium. This angle is called the critical angle, or angle of total reflection, and varies with different media. Now an effect analogous to this may take place when a ray of light is passing through different strata of air at a very small angle, which at last becomes reduced to a degree or part of a degree which may be called the critical angle. Suppose the aerial strata in fig. 1 to decrease in density from a to d; a ray of light coming from the object will be refracted from the perpendicular in passing downward through the stratum a, still more in passing through 5, and so on until it penetrates a stratum, which we will suppose is d, where the critical angle is reached, and the ray. becomes totally reflected.

The direction of the ray will then be upward, but will be refracted toward the perpendicular as it passes through successive strata of increasing density, so that when the ray reaches the eye the object will appear in the direction of e. In the second case, which takes place over the surface of water, and where the lower strata of air are cooled by the water so as to be denser than the upper, the course of the rays is shown in the exaggerated drawing in fig. 2. A vessel which may be so distant as to be partly or entirely hidden by the curvature of the earth, will appear inverted above the horizon when the rays of light are at first refracted from the perpendicular until the critical angle is reached at the stratum d, when total reflection takes place, by which the ray is given an inclination downward, so that the object appears in the direction of e. Simple looming, in which the object is seen in an erect position, will take place when the rays of light from it reach the eve before total reflection takes place, or before the critical angle is reached. When the object is seen both in an inverted and erect position, the case is, as has been remarked, a mixed one, and explainable by the examples already given.

When the strata are regular, the inverted will be above the erect image; but inequalities sometimes exist which cause, it is said, a contrary appearance, and lateral mirage may sometimes be produced in consequence of strata of different densities lying in a vertical position, as when a stratum of air is heated by a wall which is exposed to the rays of the sun. It is said that on the lake of Geneva boats have been seen doubled from the unequal density of two contiguous columns of air, more or less saturated with moisture, one being on the point of forming a fog. Many remarkable cases of mirage and looming have been recorded. In 1822, in the arctic regions, Captain Scoresby recognized by its inverted image in the air the ship Fame, which afterward proved to be at the moment 17 m. beyond the visible horizon of the observer. Dr. Yince, on Aug. 6, 1806, at 7 P. M., saw from Ramsgate, at which place usually only the tops of its towers are visible, the whole of Dover castle, appearing as if lifted and placed bodily on the near side of the intervening hill. So perfect was the illusion, that the hill itself could not be seen through the figure.

The phenomenon called fata Morgana is a complicated case of mirage. (See Fata Morgana).

Fig. 1. - Mirage of the Desert.

Fig. 2. - Mirage over Wntcr.