The simplest analogy for a mirage is the reflection of your face in the water. In optics, this is called a "ghost image".
Water has a different optical density and refractive index than air. Mirages work according to the same principle. The main condition for their appearance is a sharp change in the optical density of air.
Mirages are often associated with deserts, and this association is completely justified, because they appear where the surface of the earth, and therefore the layer of air above it, is highly heated. The most common mirage in the desert. sun rays. The temperature at the surface should be really high - about 60-70 ° С (sand in the desert, and sometimes even the air over the asphalt road, heats up to this temperature).
In this case, the optical beam coming from some real object is deflected in a curve in the lower layer of air, falling into your eyes, which suddenly begin to see this object upside down. It is such an inverted imaginary image of the sky that creates the illusion of a watery surface in a lifeless desert. This phenomenon is called the inferior mirage in optics. Such a picture, however, is not stable: since the heated air tends upward, the mirage can tremble, distort, or even disappear altogether.
More rare are the so-called upper mirages. The condition for their appearance is the presence of a strong temperature inversion (temperature increase with height) in a certain air layer above the earth's surface. When this happens, the rays are refracted just in this heated layer and the mirage that you see seems to float above the ground. Alas, this type of mirage also cannot be called stable, because such an unusual temperature distribution in the atmosphere does not last long.
And it is quite rare for the appearance of upper and lower mirages at the same time. They are called "Fata Morgana" - after the Morgana fairy who, according to legend, lives on the seabed and deceives travelers with ghostly visions. In this case, the rays are refracted both in the upper and lower layers of the air. As a result, you see a picture distorted beyond recognition, mistaking an ordinary stone for a skyscraper, and a rock for a medieval castle. Fata morgana can be observed in low latitudes in the immediate vicinity of the sea coast.
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This is how Anton Pavlovich Chekhov describes the appearance of Fata Morgana in his story The Black Monk: “A thousand years ago, a monk, dressed in black, walked through the desert, somewhere in Syria or Arabia … A few miles from that place where he was walking, the fishermen saw another black monk moving slowly along the surface of the lake. This second monk was a mirage. Now forget all the laws of optics that the legend does not seem to recognize, and listen further. From the mirage, another mirage turned out, then from another a third, so that the image of a black monk began to endlessly be transmitted from one layer of the atmosphere to another. He was seen now in Africa, then in Spain, then in India, then in the Far North …"
Another very surprising optical phenomenon is refraction, which, on the contrary, occurs at high latitudes, in the circumpolar regions. Refraction is nothing more than the refraction of the sun's rays in the atmosphere itself. This phenomenon allows us to see our Phenomenon of Fata Morgana daylight even when it has gone beyond the horizon. Or vice versa - even before dawn. In this case, the refraction of the rays as if lifts the image of the sun, and you see the sunrise before its actual arrival. The point here is the same: a sunbeam propagates in the air not in a straight line, but along a convex curved line.
It was the refraction that was first observed by the Dutch navigator Willem Barents on Novaya. Earth in the winter of 1596-1597. He named this phenomenon "the New Earth effect". And it is precisely in connection with this effect that the polar day at the poles can be 14 days longer than the polar night, although both day and night are "supposed" to last exactly six months here.
A remarkable and documented optical phenomenon is, among other things, the so-called Broken ghost. It is also called a mountain ghost, which in reality is nothing more than the shadow of an observer on the surface of clouds (fog) in the direction opposite to the sun. The shadow may appear to the observer as a very Brocken ghost, large and sometimes surrounded by colored rings, it is also able to "wiggle" (sometimes completely unexpectedly) due to the movement of the cloud layer and fluctuations in density in the cloud. The Brocken Ghost can be seen in the mountains during fog or cloudy weather, or even from an airplane. This phenomenon gained fame thanks to the Brocken peak, which is in the mountains in Germany. Constant fogs and the availability of low altitudes allow it to be seen very often.
Perhaps, it is precisely mirages that can explain many other evidences of the appearance of "ghosts" or, for example, UFOs?