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Mirage

Mirage

Overview

A mirage is a naturally occurring optical phenomenon
Optical phenomenon
An optical phenomenon is any observable event that results from the interaction of light and matter. See also list of optical topics and optics. A mirage is an example of an 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
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

 mirage, from the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 mirare, meaning "to look at, to wonder at". This is the same root as for "mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

" and "to admire".

In contrast to a hallucination
Hallucination
A hallucination, in the broadest sense of the word, is a perception in the absence of a stimulus. In a stricter sense, hallucinations are defined as perceptions in a conscious and awake state in the absence of external stimuli which have qualities of real perception, in that they are vivid,...

, a mirage is a real optical phenomenon which can be captured on camera, since light rays actually are refracted to form the false image at the observer's location.
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Encyclopedia

A mirage is a naturally occurring optical phenomenon
Optical phenomenon
An optical phenomenon is any observable event that results from the interaction of light and matter. See also list of optical topics and optics. A mirage is an example of an 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
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

 mirage, from the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 mirare, meaning "to look at, to wonder at". This is the same root as for "mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

" and "to admire".

In contrast to a hallucination
Hallucination
A hallucination, in the broadest sense of the word, is a perception in the absence of a stimulus. In a stricter sense, hallucinations are defined as perceptions in a conscious and awake state in the absence of external stimuli which have qualities of real perception, in that they are vivid,...

, a mirage is a real optical phenomenon which can be captured on camera, since light rays actually are refracted to form the false image at the observer's location. What the image appears to represent, however, is determined by the interpretive faculties of the human mind. For example, inferior images on land are very easily mistaken for the reflections from a small body of water.

Mirages can be categorized as "inferior" (meaning lower), "superior" (meaning higher) and "Fata Morgana
Fata Morgana (mirage)
A Fata Morgana is an unusual and very complex form of mirage, a form of superior mirage, which, like many other kinds of superior mirages, is seen in a narrow band right above the horizon...

", one kind of superior mirage consisting of a series of unusually elaborate, vertically-stacked images, which form one rapidly-changing mirage.

Cause


Cold air is denser than warm air and has therefore a greater refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

. As light passes from colder air across a sharp boundary to significantly warmer air, the light rays bend away from the direction of the temperature gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

. When light rays pass from hotter to colder, they bend toward the direction of the gradient. If the air near the ground is warmer than that higher up, the light ray bends in a concave, upward trajectory.

Once the rays reach the viewer’s eye, the visual cortex interprets it as if it traces back along a perfectly straight "line of sight". This line is however at a tangent to the path the ray takes at the point it reaches the eye. The result is that an "inferior image" of the sky above appears on the ground. The viewer may incorrectly interpret this sight as water which is reflecting the sky, which is, to the brain, a more reasonable and common occurrence.

In the case where the air near the ground is cooler than that higher up, the light rays curve downward, producing a "superior image".

The "resting" state of the Earth's atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

 has a vertical gradient of about -1° Celsius
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...

 per 100 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s of altitude. (The value is negative because it gets colder as altitude increases.) For a mirage to happen, the temperature gradient
Temperature gradient
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length...

 has to be much greater than that. According to Minnaert, the magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....

 of the gradient needs to be at least 2°C per metre, and the mirage does not get strong until the magnitude reaches 4º or 5°C per metre. These conditions do occur when there is strong heating at ground level, for example when the sun has been shining on sand
Sand
Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...

 or asphalt
Asphalt concrete
Asphalt concrete is a composite material commonly used in construction projects such as road surfaces, airports and parking lots. It consists of asphalt and mineral aggregate mixed together, then laid down in layers and compacted...

 and an inferior image is commonly generated because of this.

Inferior mirage


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
Desert
A desert is a landscape or region that receives an extremely low amount of precipitation, less than enough to support growth of most plants. Most deserts have an average annual precipitation of less than...

 it appears as a lake of water. On tarmac
Tarmac
Tarmac is a type of road surface. Tarmac refers to a material patented by Edgar Purnell Hooley in 1901...

 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 arrive lower 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
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

) 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.

Highway mirage



A highway mirage is an inferior mirage which can be seen very commonly on roadways by day or by night. This hot-road mirage is usually most noticeable on hot sunny days. It seems to look like a 'pool', however when you get closer you realise that it actually isn't there.
Warm air is less dense than cool air, and the variation between the hot air at the surface of the road and the denser cool air above it creates a gradient
Gradient index optics
Gradient-index optics is the branch of optics covering optical effects produced by a gradual variation of the refractive index of a material. Such variations can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses...

 in the refractive index of the air. Light from the sky
Sky
The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...

 at a shallow angle to the road is refracted
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 by the index gradient, making it appear as if the sky is reflected by the road's surface. The mind interprets this as a pool of water on the road, since water also reflects the sky.

Superior mirage


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 temperature gradient of the atmosphere. In this case the light rays are bent down and so the image appears above the true object, hence the name superior. Superior mirages 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 or warm air to move down.

Superior mirages are most common in polar region
Polar region
Earth's polar regions are the areas of the globe surrounding the poles also known as frigid zones. The North Pole and South Pole being the centers, these regions are dominated by the polar ice caps, resting respectively on the Arctic Ocean and the continent of Antarctica...

s, especially over large sheets of ice with a uniform low temperature. They also occur at more moderate latitudes, although in those cases they are weaker and less smooth and stable. For example, a distant shoreline may appear to tower and look higher (and thus perhaps closer) than it really is. Because of the turbulence, there seem to be dancing spikes and towers. This type of mirage is also called the Fata Morgana
Fata Morgana (mirage)
A Fata Morgana is an unusual and very complex form of mirage, a form of superior mirage, which, like many other kinds of superior mirages, is seen in a narrow band right above the horizon...

 or hillingar in the Icelandic language
Icelandic language
Icelandic is a North Germanic language, the main language of Iceland. Its closest relative is Faroese.Icelandic is an Indo-European language belonging to the North Germanic or Nordic branch of the Germanic languages. Historically, it was the westernmost of the Indo-European languages prior to the...

.

A superior mirage can be right-side 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.

Superior mirages can have a striking effect due to the Earth's curvature. Were the Earth flat, light rays that bend down would soon hit the ground and only nearby objects would be affected. Since Earth is round, if their downward bending curve is about the same as the curvature of the Earth
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

, light rays can travel large distances, perhaps from beyond the horizon. This was observed and documented for the first time in 1596, when a ship under the command of Willem Barents
Willem Barents
Willem Barentsz was a Dutch navigator, cartographer, explorer, and a leader of early expeditions to the far north....

 in search of the Northeast passage became stuck in the ice at Novaya Zemlya
Novaya Zemlya
Novaya Zemlya , also known in Dutch as Nova Zembla and in Norwegian as , is an archipelago in the Arctic Ocean in the north of Russia and the extreme northeast of Europe, the easternmost point of Europe lying at Cape Flissingsky on the northern island...

. The crew was forced to endure the polar winter there. They saw their midwinter night come to an end with the rise of a distorted Sun about two weeks earlier than expected. It was not until the 20th century that science could explain the reason: The real Sun had still been below the horizon, but its light rays followed the curvature of the Earth. This effect is often called a Novaya Zemlya mirage
Novaya Zemlya effect
The Novaya Zemlya effect is a polar mirage caused by high refraction of sunlight between atmospheric thermoclines. The Novaya Zemlya effect will give the impression that the sun is rising earlier than it actually should and depending on the meteorological situation the effect will present the sun...

. For every 111.12 kilometres (69 mi) 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 that are in reality so far away that they should not be 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 +12.9°C per 100 meters (where the positive sign means temperature gets hotter as one goes higher), then horizontal light rays will just follow the curvature of the Earth, and the horizon will appear flat. If the gradient is less (as it almost always is) the rays are not bent enough and get lost in space, which is the normal situation of a spherical, convex "horizon".

In some situations, distant objects can get elevated or lowered, stretched or shortened with no mirage involved.

Fata Morgana




A Fata Morgana, the name of which comes from the Italian translation of Morgan le Fay
Morgan le Fay
Morgan le Fay , alternatively known as Morgane, Morgaine, Morgana and other variants, is a powerful sorceress in the Arthurian legend. Early works featuring Morgan do not elaborate her character beyond her role as a fay or magician...

, the fairy shapeshifting half-sister of King Arthur, is a very complex superior mirage. It appears with alternations of compressed and stretched zones, erect images and inverted images. A Fata Morgana is also a fast-changing mirage.

Fata Morgana mirages are most common in polar region
Polar region
Earth's polar regions are the areas of the globe surrounding the poles also known as frigid zones. The North Pole and South Pole being the centers, these regions are dominated by the polar ice caps, resting respectively on the Arctic Ocean and the continent of Antarctica...

s, especially over large sheets of ice with a uniform low temperature, but they can be observed almost anywhere. While in polar regions a Fata Morgana may be observed on cold days, in desert areas and over oceans and lakes a Fata Morgana may be observed on hot days. For a Fata Morgana, temperature inversion has to be strong enough that light rays' curvatures within the inversion are stronger than the curvature of the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

.

The rays will bend and create arc
Arc (geometry)
In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle...

s. An observer needs to be within an atmospheric duct
Atmospheric duct
In telecommunication, an atmospheric duct is a horizontal layer in the lower atmosphere in which the vertical refractive index gradients are such that radio signals are guided or ducted, tend to follow the curvature of the Earth, and experience less attenuation in the ducts than they would if...

 in order to be able to see a Fata Morgana.
Fata Morgana mirages may be observed from any altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

 within the Earth's
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 atmosphere
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

, including from mountaintops or airplanes.

A Fata Morgana can go from superior to inferior mirage and back within a few seconds, depending on the constantly changing conditions of the atmosphere. Sixteen frames of the mirage of the Farallon Islands
Farallon Islands
The Farallon Islands, or Farallones , are a group of islands and sea stacks in the Gulf of the Farallones, off the coast of San Francisco, California, USA. They lie outside the Golden Gate and south of Point Reyes, and are visible from the mainland on clear days...

, which cannot be seen from sea level at all under normal conditions because they are located below the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...

, were photographed on the same day. The first fourteen frames have elements of a Fata Morgana display—alternations of compressed and stretched zones. The last two frames were photographed a few hours later around sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...

. The air was cooler while the ocean was probably a little bit warmer, which made temperature inversion lower. The mirage was still present, but it was not as complex as it had been a few hours before sunset, and it corresponded no longer to a Fata Morgana but rather to a superior mirage display.

Distortions of image and bending of light can produce spectacular effects. In his book Pursuit: The Chase and Sinking of the "Bismarck", the author Ludovic Kennedy describes an incident that allegedly took place below the Denmark Strait during 1941, following the sinking of the Hood. The Bismarck
German battleship Bismarck
Bismarck was the first of two s built for the German Kriegsmarine during World War II. Named after Chancellor Otto von Bismarck, the primary force behind the German unification in 1871, the ship was laid down at the Blohm & Voss shipyard in Hamburg in July 1936 and launched nearly three years later...

, while pursued by the British cruisers Norfolk and Suffolk, passed out of sight into a sea mist. Within a matter of seconds, the ship re-appeared steaming toward the British ships at high speed. In alarm the cruisers separated, anticipating an imminent attack, and observers from both ships watched in astonishment as the German battleship fluttered, grew indistinct and faded away. Radar watch during these events indicated that the Bismarck had in fact made no changes of course.

Mirage of astronomical objects



A mirage of an astronomical object is a naturally-occurring optical phenomenon
Optical phenomenon
An optical phenomenon is any observable event that results from the interaction of light and matter. See also list of optical topics and optics. A mirage is an example of an optical phenomenon....

, in which light rays are bent to produce distorted or multiple images of an astronomical object
Astronomical object
Astronomical objects or celestial objects are naturally occurring physical entities, associations or structures that current science has demonstrated to exist in the observable universe. The term astronomical object is sometimes used interchangeably with astronomical body...

. The mirages might be observed for such astronomical objects as the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

, the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

, the planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s, bright star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s and very bright comet
Comet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...

s. The most commonly observed are sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...

 and sunrise
Sunrise
Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Sunrise should not be confused with dawn, which is the point at which the sky begins to lighten, some time before the sun itself appears, ending twilight...

 mirages.

See also


  • Atmospheric refraction
    Atmospheric refraction
    Atmospheric refraction is the deviation of light or other things like humanelectromagnetic wave from a straight line as it passes through the atmosphere due to the variation in air density as a function of altitude...

  • Looming and similar refraction phenomena
    Looming and similar refraction phenomena
    While mirages are the best known atmospheric refraction phenomena, looming and similar refraction phenomena do not produce mirages. Mirages show an extra image or images of the miraged object, while looming, towering, stooping, and sinking do not. No inverted image is present in those phenomena...

  • Mirage of astronomical objects
    Mirage of astronomical objects
    A mirage of an astronomical object is a naturally occurring optical phenomenon, in which light rays are bent to produce distorted or multiple images of an astronomical object. The mirages might be observed for such astronomical objects as the Sun, the Moon, the planets, bright stars and very...

  • Novaya Zemlya effect
    Novaya Zemlya effect
    The Novaya Zemlya effect is a polar mirage caused by high refraction of sunlight between atmospheric thermoclines. The Novaya Zemlya effect will give the impression that the sun is rising earlier than it actually should and depending on the meteorological situation the effect will present the sun...

  • Refraction
    Refraction
    Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...


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