In optics, the deceptive appearance of a distant object caused by the bending of light rays (refraction) in layers of air of varying density. Under certain conditions, such as over a stretch of pavement or desert air heated by intense sunshine, the air cools rapidly with elevation and therefore increases in density and refractive power. Sunlight reflected down from the upper portion of an object will be directed through the cool air in the normal way; although the light would not be seen ordinarily because of the angle, it curves upward after it enters the rarefied hot air near the ground, thus being refracted to the observer's eye as though it had originated below the heated surface. When the sky is the object of the mirage, the land is mistaken for a lake or sheet of water.
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A mirage is a naturally-occurring optical phenomenon, in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning 'to look at, to wonder at'. This is the same root as for mirror and to admire. Like a mirror, a mirage shows images of things which are elsewhere. The principal physical cause of a mirage, however, is refraction rather than reflection. A mirage is a real optical phenomenon that can be captured on camera, since light rays actually are refracted to form the false image at the observer's location. The interpretation of the image, however, is up to the fantasy of the human mind, and is easily mistaken for a small puddle of water.
Cold air is denser than warm air, and has therefore a greater refractive index. As light passes from colder air to warmer air it bends away from the direction of the temperature gradient (the "normal" in the figure on the left); when it passes from hotter to colder, it bends towards the direction of the gradient. The diagram on the left shows a light ray coming from the sky toward the hot ground. If the air near the ground is warmer than that higher up, the light ray bends in a concave upwards trajectory. Once the ray reaches the viewer’s eye, the eye traces it as the line of sight, which is the line tangent to the path the ray takes at the point it reaches the eye. The result is that an inferior image for the above sky appears on the ground. The viewer may incorrectly interpret this sight as water reflecting the sky. In the case where the air near the ground is cooler than that higher up, the light rays will of course curve downwards, producing a superior image.
The 'rest' state of the Earth's atmosphere is with a vertical gradient of about -1 degree Celsius per 100 metres height. (The value is negative because it gets colder when you go higher.) For an actual mirage to happen, the temperature gradient has to be much greater. According to Minnaert the magnitude of the gradient should be at least 2°C per meter, and the mirage will not get strong until the magnitude reaches 4 or 5°C per meter. These conditions can occur when there is strong heating at ground level, for example when the sun is shining on sand or asphalt.
The model given above explains the cause of the inferior mirage, called inferior because the image seen is under the real object. The real object is the (blue) sky or any distant object in that direction, meaning we see a bright bluish patch on the ground in the distance. For exhausted travelers in the desert it appears as a lake of water. On tarmac roads it may seem that water or even oil has been spilled. This is called a desert mirage or highway mirage. Note that both sand and tarmac can become very hot when exposed to the sun, easily being more than 10°C hotter than the air one meter above, enough to cause the mirage.
Light rays coming from a particular distant object all travel through nearly the same air layers and all are bent over about the same amount. Therefore rays coming from the top of the object will come less high than those from the bottom. The image usually is upside down, enhancing the illusion that the sky image seen in the distance is really a water or oil puddle acting as a mirror.
Inferior images are not stable. Hot air rises, and cooler air (being more dense) descends, so the layers will mix, giving rise to turbulence. The image will be distorted accordingly. It may be vibrating; it may be vertically extended (towering) or horizontally extended (stooping). If there are several temperature layers, several mirages may mix together, perhaps causing double images. In any case, mirages are usually not larger than about half a degree high (same apparent size as the sun and moon) and from objects only a few kilometers away.
A superior mirage occurs when the air below the line of sight is colder than that above. This is called a temperature inversion, since it does not represent the normal equilibrium temperature gradient of the atmosphere. Since in this case the light rays are bent down, the image appears above the true object, hence the name superior. They are in general less common than inferior mirages, but when they do occur they tend to be more stable, as cold air has no tendency to move up and warm air no tendency to move down.
Superior mirages are most common in polar regions, especially over large sheets of ice with a uniform low temperature. They also occur at more moderate latitudes, however, although in that case they are weaker and not so smooth. For example a distant shoreline may be made towering, looking higher (and thus perhaps closer) than it is in reality, but because of the turbulences there seem to be dancing spikes, towers and so forth. This type of mirage is also called the Fata Morgana or in Icelandic halgerndingar.
Superior images can be straight up or upside down, depending on the distance of the true object and the temperature gradient. Often the image appears as a distorted mixture of up and down parts.
If the Earth were flat, superior images would not be interesting. Light rays which bent down would soon hit the ground, and only close objects would be affected. Since the Earth is round, if the amount of downward bending is about equal to the curvature of the Earth, light rays can travel large distances, perhaps from beyond the horizon. This was observed for the first time in 1596, when a ship under the command of Willem Barents looking for the Northeast passage got stuck in the ice at Novaya Zemlya and the crew had to endure the polar winter there. They saw their midwinter night ending with the rise of a distorted sun about 2 weeks earlier than expected. It was not until the 20th century that Europeans understood the reason: that the real sun had still been under their horizon, but its light rays followed the curvature of the Earth. This effect is often called a Novaya Zemlya mirage. For every 100 km the light rays can travel parallel to the Earth's surface, the sun will appear 1° higher on the horizon. The inversion layer must have just the right temperature gradient over the whole distance to make this possible.
In the same way ships which are in reality so far away that they should not have been visible above the geometric horizon, may appear on the horizon, or even above the horizon as superior mirages. This may explain some stories about flying ships or coastal cities in the sky, as described by some polar explorers. These are examples of so called Arctic mirages or hillingar in Icelandic.
If the vertical temperature gradient is +11°C per 100 meters (reminder: positive means getting hotter when going up), horizontal light rays will just follow the curvature of the Earth, and the horizon will appear flat. If the gradient is less the rays are not bent enough, and get lost in space. That is the normal situation of a spherical, convex horizon. But if the gradient gets larger, say 18°C per 100 meters, the observer will see the horizon turned upwards, being concave, as if he were standing on the bottom of a saucer.