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Various kinds of mirages in one location taken over the course of six minutes, not shown in chronological order.[a]

A mirage is a naturally occurring optical phenomenon in which light rays bend via refraction to produce a displaced image of distant objects or the sky.[1] The word comes to English via the French (se) mirer, from the Latin mirari, meaning "to look at, to wonder at".[2]

Mirages can be categorized as "inferior" (meaning lower), "superior" (meaning higher) and "Fata Morgana", one kind of superior mirage consisting of a series of unusually elaborate, vertically stacked images, which form one rapidly changing mirage.

In contrast to a hallucination, a mirage is a real optical phenomenon that can be captured on camera, since light rays are actually 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.

Inferior mirage

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A schematic of an inferior mirage, showing a) the unrefracted line of sight, b) the refracted line of sight and c) the apparent position of the refracted image.

In an inferior mirage, the mirage image appears below the real object. The real object in an inferior mirage is the (blue) sky or any distant (therefore bluish) object in that same direction. The mirage causes the observer to see a bright and bluish patch on the ground.

Light rays coming from a particular distant object all travel through nearly the same layers of air, and all are refracted at about the same angle. Therefore, rays coming from the top of the object will arrive lower than those from the bottom. The image is usually upside-down, enhancing the illusion that the sky image seen in the distance is a specular reflection on a puddle of water or oil acting as a mirror.

While the aero-dynamics are highly active, the image of the inferior mirage is stable, unlike the fata morgana, which can change within seconds. Since warmer air rises while cooler air (being denser) sinks, the layers will mix, causing turbulence. The image will be distorted accordingly; it may vibrate or be stretched vertically (towering) or compressed vertically (stooping). A combination of vibration and extension are also possible. If several temperature layers are present, several mirages may mix, perhaps causing double images. In any case, mirages are usually not larger than about half a degree high (roughly the angular diameter of the Sun and Moon) and are from objects between dozens of meters and a few kilometers away.

Heat haze

[edit]
See also: Schlieren, Twinkling, and Astronomical seeing
A hot-road mirage, in which "fake water" appears on the road, is the most commonly observed instance of an inferior mirage.
Heat haze seen through exhaust gas from a jet engine

Heat haze, also called heat shimmer, refers to the inferior mirage observed when viewing objects through a mass of heated air. Common instances when heat haze occurs include images of objects viewed across asphalt concrete (also known as tarmac), roads, and over masonry rooftops on hot days, above and behind fire (as in burning candles, patio heaters, and campfires), and through exhaust gases from jet engines. When appearing on roads due to the hot asphalt, it is often referred to as a "highway mirage". It also occurs in deserts; in that case, it is referred to as a "desert mirage". Both tarmac and sand can become very hot when exposed to the sun, easily being more than 10 °C (18 °F) higher than the air a meter (3.3 feet) above, enough to make conditions suitable to cause the mirage.

Convection causes the temperature of the air to vary, and the variation between the hot air at the surface of the road and the denser cool air above it causes a gradient in the refractive index of the air. This produces a blurred shimmering effect, which hinders the ability to resolve the image and increases when the image is magnified through a telescope or telephoto lens.

Light from the sky at a shallow angle to the road is refracted by the index gradient, making it appear as if the sky is reflected by the road's surface. This might appear as a pool of liquid (usually water, but possibly others, such as oil) on the road, as some types of liquid also reflect the sky. The illusion moves into the distance as the observer approaches the miraged object giving one the same effect as approaching a rainbow.

Heat haze is not related to the atmospheric phenomenon of haze.

Superior mirage

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Comparison of inferior and superior mirages due to differing air refractive indices n
Above: A superior mirage of a plane on ice, McMurdo Station

Right: An artificial mirage, using sugar solutions to simulate the inversion layers.[b]

A superior mirage is one in which the mirage image appears to be located above the real object. A superior mirage occurs when the air below the line of sight is colder than the air above it. This unusual arrangement is called a temperature inversion. During the daytime, the normal temperature gradient of the atmosphere is cold air above warm air. Passing through the temperature inversion, the light rays are bent down, and so the image appears above the true object, hence the name superior.[3]

Superior mirages are quite common in polar regions, especially over large sheets of ice that have a uniform low temperature. Superior mirages also occur at more moderate latitudes; however, in those cases, they are weaker and tend to be 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 appear to be dancing spikes and towers. This type of mirage is also called the Fata Morgana, or hafgerðingar in the Icelandic language.[4]

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.

Since the earth is round, if the downward bending curvature of light rays is about the same as the curvature of Earth, light rays can travel large distances, including from beyond the horizon. This was observed and documented in 1596, when a ship in search of the Northeast passage became stuck in the ice at Novaya Zemlya, above the Arctic Circle. The Sun appeared to rise two weeks earlier than expected; the real Sun was still visible below the horizon, but its light rays followed the curvature of Earth. This effect is often called a Novaya Zemlya mirage. For every 111.12 kilometres (69.05 mi) that light rays travel parallel to 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 so far away that they should not be visible above the geometric horizon may appear on or even above the horizon as superior mirages.[5] 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.

Illustration in a 1872 book to describe a mirage

If the vertical temperature gradient is +12.9 °C (23.2 °F) per 100 meters/330 feet (where the positive sign means the temperature increases at higher altitudes) then horizontal light rays will just follow the curvature of 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 be elevated or lowered, stretched or shortened with no mirage involved.

Fata Morgana

[edit]
Main article: Fata Morgana (mirage)

A Fata Morgana (the name comes from the Italian translation of Morgan le Fay, the fairy, shapeshifting half-sister of King Arthur) is a very complex superior mirage. It appears with alternations of compressed and stretched areas, erect images, and inverted images.[6] A Fata Morgana is also a fast-changing mirage.

Fata Morgana mirages are most common in polar regions, especially over large sheets of ice with a uniform low temperature, but they can be observed almost anywhere. 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 Earth.[6]

The rays will bend and form arcs. An observer needs to be within an atmospheric duct to be able to see a Fata Morgana.[7] Fata Morgana mirages may be observed from any altitude within Earth's atmosphere, including from mountaintops or airplanes.[8][9]

Distortions of image and bending of light can produce spectacular effects. In his book Pursuit: The Chase and Sinking of the "Bismarck", Ludovic Kennedy describes an incident that allegedly took place below the Denmark Strait during 1941, following the sinking of the Hood. The Bismarck, 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 change to her course.

Sequence of a Fata Morgana of the Farallon Islands as seen from San Francisco
The same sequence as an animation

Night-time mirages

[edit]

The conditions for producing a mirage can occur at night as well as during the day. Under some circumstances mirages of astronomical objects and mirages of lights from moving vehicles, aircraft, ships, buildings, etc. can be observed at night.[1]

Mirage of astronomical objects

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Main article: 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. Mirages can be observed for such astronomical objects as the Sun, the Moon, the planets, bright stars, and very bright comets. The most commonly observed are sunset and sunrise mirages.

See also

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Notes

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References

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Bibliography

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Mirage

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from Grokipedia
A mirage is a naturally occurring in which rays are bent, or refracted, due to variations in the caused by gradients, resulting in the apparent displacement or of distant objects. These effects are real physical occurrences rooted in , not mere illusions, and are most commonly observed in environments with significant differences, such as hot deserts or over paved roads. Mirages arise from the of as it passes through layers of air with differing refractive indices, which bend the rays in curved paths rather than straight lines. Mirages are broadly classified into two main types: inferior and superior, each depending on the direction of the in the atmosphere. An inferior mirage occurs when a layer of warmer, less dense air lies beneath cooler air, causing rays from an object to bend upward in a convex curve; this produces an inverted image appearing below the actual object, such as the shimmering "" seen on hot asphalt roads during summer. In contrast, a superior mirage forms under a temperature inversion where colder air is trapped below warmer air, leading to concave bending of rays downward and creating erect or multiple distorted images above the true position of the object; these are often observed over cold seas or polar regions, sometimes magnifying distant ships or icebergs to appear as towering, ethereal structures. Beyond these primary forms, complex mirages can combine elements of both types or involve additional atmospheric layers, leading to phenomena like the Fata Morgana, a superior mirage variant that creates elongated, castle-like illusions over horizons. Mirages have been documented and studied since ancient times, with scientific explanations emerging in the 19th century through principles of ray optics and Snell's law, and they continue to influence fields like meteorology, navigation, and even astronomy by distorting celestial observations near the horizon. Understanding mirages highlights the intricate interplay between light, temperature, and air density in shaping our perception of the environment.

Fundamentals

Definition and Characteristics

A mirage is a naturally occurring optical phenomenon caused by atmospheric refraction, in which light rays bend through layers of air with differing temperatures and densities, producing displaced or distorted images of distant objects or the sky. These effects often manifest as illusory pools of water in deserts, shimmering horizons, or apparent inversions, creating the perception of something present that is not in the expected location. Unlike true reflections from surfaces, mirages arise solely from the gradual curving of light paths due to refractive index variations. Key characteristics of mirages include their illusory yet physically real nature, where the image stems from actual rays but misleads the observer's interpretation of and position. The appearance is highly dependent on the observer's vantage point, frequently shifting or disappearing with even slight changes in position or angle. Their duration is inherently temporary, persisting only as long as the atmospheric conditions—such as stable temperature gradients—maintain the , and they differ from hallucinations by being verifiable external optical events rather than internal perceptual fabrications. The word "" originates from the 16th-century French mirage, derived from se mirer meaning "to be reflected," which traces back to the Latin mirari, "to wonder at," evoking the astonishment inspired by these visions; it entered English around 1812 to describe such optical effects. For optimal , mirages are most visible on clear days with pronounced contrasts near the surface, such as hot ground under cooler air, typically over flat horizons like roads or seas where the bending of light is evident from afar.

Physical Causes

Mirages arise from the of as it passes through the Earth's atmosphere, where variations in air cause rays to bend along curved paths rather than traveling in straight lines. This bending occurs because the of air, which determines how much slows down and changes direction, varies with air ; denser air has a higher . According to , the relationship between the angles of incidence and refraction at an interface between two media is given by n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2, where nn is the and θ\theta the angle relative to the normal; in a continuously varying medium like the atmosphere, this leads to gradual deviation of ray paths. Temperature gradients in the atmosphere are the primary driver of these variations, as warmer air is less than cooler air, creating layered regions with differing refractive indices. When rays traverse such , they experience a continuous change in speed—slower in denser (cooler) layers and faster in rarer (warmer) layers—resulting in upward or downward curvature depending on the 's direction. For instance, a negative gradient (temperature decreasing with height) causes rays to curve concave upward, while a positive gradient (temperature increasing with height) produces concave downward curvature. This differential distorts the apparent position of distant objects, forming illusory images. In certain conditions with sharp density interfaces, can approach effects similar to , where light rays incident at angles greater than the critical angle—defined as θc=sin⁡−1(n2/n1)\theta_c = \sin^{-1}(n_2 / n_1) for n2<n1n_2 < n_1—are reflected back into the originating medium without transmission. Although mirages typically involve gradual gradients rather than discrete boundaries, steep temperature contrasts can create mirage-like trapping of rays, enhancing the illusion by preventing direct line-of-sight transmission./University_Physics_III_-Optics_and_Modern_Physics(OpenStax)/01:_The_Nature_of_Light/1.05:_Total_Internal_Reflection) Atmospheric stability plays a crucial role in amplifying these refractive effects through temperature inversions (where temperature increases with height, stabilizing the air) or lapses (temperature decreases with height, promoting instability). Inversions trap cooler, denser air near the surface, steepening gradients and causing pronounced ray bending; conversely, strong lapse rates near hot ground enhance downward curvature. Ray tracing simulations illustrate this: a light ray from a distant object enters a gradient layer, bends continuously according to local refractive index, and may reach the observer after following an arcuate path, appearing to originate from an impossible location. Such inversions are common over cold water or in calm conditions, intensifying superior mirages, while lapse rates dominate in heated desert or road scenarios for inferior types.

Inferior Mirages

Appearance and Formation

Inferior mirages form when a layer of warm air lies adjacent to a hot surface, such as pavement or desert sand, overlain by cooler air at higher altitudes, resulting in a decrease in air density near the surface. This configuration creates a vertical gradient in air density, with the refractive index of air decreasing downward toward the less dense warm layer. Light rays from distant objects or the sky traveling through this gradient experience refraction that bends them upward in a convex curve relative to the surface, effectively placing the apparent position of the images below their true location. In inferior mirages, rays curve upward away from the less dense warm air near hot surfaces, producing inverted images below the horizon rather than above it. The visual appearance of an inferior mirage typically features distant objects or the sky appearing inverted and displaced below the actual position, often resembling a shimmering pool of water on the ground. These distortions create the illusion of a reflective surface, where the "reflection" is actually the inverted image of the sky or object, vertically compressed, with a vanishing line limiting visibility of lower parts. The images remain inverted but can exhibit shimmering oscillations under turbulent conditions, enhancing the watery effect observed by viewers. Such mirages require strong temperature gradients near the surface, commonly occurring over hot deserts, paved roads, or calm warm waters during clear weather. The ray paths follow a curvature governed by the refractive index gradient, where the local radius of curvature rr for a horizontal ray is given by r=ndndhr = \frac{n}{\frac{dn}{dh}}, with dndh>0\frac{dn}{dh} > 0 leading to upward bending. This refraction mechanism, rooted in Snell's law applied across varying densities, is enhanced by minimal turbulence to maintain clarity.

Everyday Examples

In deserts like the , inferior mirages frequently manifest as illusory oases or pools of water on the horizon, a that has historically misled travelers by promising in arid conditions. Colonial-era accounts from the describe European explorers in the encountering these deceptive images, which reinforced perceptions of the desert as a treacherous, illusory landscape that mirrored and distorted their own expectations. Similar reports emerge from the Australian outback, where 19th-century expeditions faced apparent water sources that evaporated upon closer inspection, exacerbating and disorientation during overland treks. A common everyday example occurs on hot asphalt roads during summer, where the pavement appears covered in shimmering due to the inferior mirage effect from heat rising off the surface. This illusion is frequently captured on traffic cameras, showing drivers approaching what looks like wet patches that vanish as they near, often leading to unnecessary braking or lane changes. In urban settings, intensified by heat islands from and , these mirages become more prevalent, as documented in recent analyses of gradients post-2020. Over calm seas with warmer , inferior mirages can make distant ships appear to float unnaturally on a reflective layer, blending their hulls with the sky in a water-like shimmer. This effect, observed by mariners, alters perceived distances and elevations, sometimes complicating in coastal waters. Such mirages pose practical risks, including driving hazards where illusions prompt evasive maneuvers, potentially contributing to collisions on highways. In over hot terrain, they can obscure actual conditions, masking puddles or soft spots and increasing risks, as noted in pilot reports from hazy, high-temperature environments.

Superior Mirages

Appearance and Formation

Superior mirages form when a layer of cold air lies adjacent to a colder surface, such as or , overlain by warmer air at higher altitudes, resulting in a temperature inversion. This configuration creates a vertical in air density, with the of air increasing downward toward the denser cold layer. Light rays from distant objects traveling through this experience that bends them downward in a convex curve relative to the surface, effectively elevating the apparent position of the objects above their true location. Unlike inferior mirages, where rays curve upward toward less dense warm air near hot surfaces, superior mirage rays bend toward the denser medium below, producing images above the horizon rather than below it. The visual appearance of a superior mirage typically features distant objects, such as ships or landforms, appearing stretched vertically or hovering elevated above the horizon. These distortions often resemble pencil-like elongations or effects, where hidden portions of objects below the geometric horizon become visible due to the upward deflection of . The images remain upright in simple cases but can exhibit subtle oscillations or multiple layers under stable conditions, enhancing the ethereal quality observed by viewers. Such mirages require stable temperature inversions, commonly occurring in polar regions over or in temperate areas above cold lakes during calm weather. The ray paths follow a governed by the gradient, where the local rr for a horizontal ray is given by r=ndndhr = \frac{n}{\frac{dn}{dh}}, with dndh<0\frac{dn}{dh} < 0 leading to downward bending. This mechanism, rooted in applied across varying densities, demands minimal to maintain clarity.

Fata Morgana

The Fata Morgana is a complex variant of the superior mirage, featuring multiple, highly distorted images of terrestrial objects that appear elevated, inverted, or fragmented, often resembling ethereal castles, towering cliffs, or ships floating in the sky. This arises from atmospheric ducting, where light rays from distant sources are repeatedly refracted and reflected within stratified air layers, producing a stacked series of erect and inverted replicas confined to a narrow band near the horizon. The name derives from , the legendary Arthurian sorceress, stemming from medieval Italian folklore that attributed the apparitions—frequently sighted over the —to her magical conjurings of illusory realms. Formation of the Fata Morgana requires a series of thin, alternating layers of cold and warm air in a pronounced temperature inversion, typically over cold surfaces like or , where air temperature increases sharply with height. These layered inversions create steep density gradients that bend rays into curved, oscillating trajectories, trapping them in a duct-like channel where they undergo multiple internal reflections, akin to piping through a fiber optic. Unlike simpler superior mirages, the wavy in these multi-layered ducts generates the characteristic complexity, with rays emerging at varying angles to form the superimposed, undulating images. The phenomenon is most famously associated with the between and mainland , where it has been documented since ancient times by local observers and linked to legends in medieval accounts from the onward. In polar regions, such as over ice floes, it has been noted by explorers since the during voyages through cold, inversion-prone waters. Visually, the Fata Morgana exhibits extreme vertical elongation of objects, horizontal repetitions of the inverted forms, and occasional chromatic fringes from dispersion, with displays persisting for up to several hours under stable conditions. Recent 2023 sightings, including a striking example over Scottish hills mimicking icebergs, underscore its occurrence in temperate zones during intense inversions, while polar examples continue to highlight its prevalence in cold environments.

Special Mirages

Night-time Mirages

Night-time mirages arise from of artificial light sources under conditions of strong temperature inversions, where cooler air near the ground is overlain by warmer air aloft, bending light rays upward and creating displaced images. These inversions form post-sunset as the Earth's surface radiates , cooling the while upper air remains relatively warm, often in clear, calm conditions that enhance the gradient. Unlike daytime mirages, nocturnal ones primarily affect visible lights from cities, vehicles, or ships, as the dark sky reduces background contrast but allows point sources to stand out. In appearance, these mirages often elevate distant , making them seem to float above the horizon, or produce multiple stacked images through ducting effects where is trapped and repeatedly . skylines may appear inverted or stretched vertically, with beams of extending unnaturally, while individual sources like streetlights can form elongated vertical streaks due to the path. The reduced atmospheric at night sharpens these effects compared to daylight, yielding clearer distortions visible over tens of kilometers. A prominent example is the nocturnal view of Toronto's skyline from across , where the city's illuminated buildings and appear to hover above the water, sometimes with the lower portions inverted due to a strong springtime inversion over the cold lake surface. Similarly, ship lights at have historically been observed as floating or phantom vessels, leading sailors to mistake them for distant signals or craft, as in accounts of superior mirages distorting maritime horizons. Another instance involves elevated views of prison lights in mountainous areas, where cold air drainage creates inversions that lift the images higher than their actual positions. Such mirages typically occur on clear, calm nights shortly after sunset, when inversions are strongest but light sources provide sufficient contrast against the ; they are less frequent than daytime phenomena due to the scarcity of bright natural illumination. The minimal of in low-humidity nocturnal air permits more pronounced , historically contributing to navigational errors like misidentified beacons during voyages.

Astronomical Mirages

Astronomical mirages arise from extreme near the horizon, where density gradients in the air bend light rays from celestial bodies such as the Sun or during their rise or set. These gradients, often resulting from inversions or varying humidity, cause the light to follow curved paths, distorting the apparent position and shape of the objects. Unlike uniform higher in the sky, the intensified bending at low altitudes amplifies the effect, making it particularly prominent for observers near . The most common appearances include a flattened or oval-shaped Sun or , as differential compresses the vertical dimension more than the horizontal. A striking variant is the , a momentary emerald ray or spot emerging from the upper limb of the setting Sun, caused by the dispersion of sunlight into colors combined with mirage compression of the solar disk. This flash typically lasts 1-2 seconds and demands a sharp, unobstructed horizon for visibility, often over calm seas. Another phenomenon, the Novaya Zemlya effect, involves superior mirage-like in polar regions, trapping sunlight below a inversion layer and extending the perceived polar day or night by allowing the Sun to appear above the horizon when it is geometrically below. These effects can be predicted using tables, which provide corrections to the apparent altitude of celestial bodies. For instance, near the horizon, the correction δ\delta is approximately 0.57° under standard conditions. A common approximation is δ≈1tan⁡(h+7.31h+4.4)\delta \approx \frac{1}{\tan\left(h + \frac{7.31}{h + 4.4}\right)} arcminutes, where hh is the true altitude in degrees. Observations of astronomical mirages are frequent at , where stable atmospheric layers enhance clarity, and have been documented since Aristotle's Meteorologica in the BCE, where he described effects akin to mirages. Modern photography routinely captures these distortions, including time-lapse sequences of squashed Moons and verified green flashes, confirming the phenomena's optical nature.

References

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