An Introduction to Mirages

Introduction

First of all, what's a mirage? Mirages are not optical illusions, as many people (and Web sites!) think. They are real phenomena of atmospheric optics, caused by strong ray-bending in layers with steep thermal gradients. Because mirages are real physical phenomena, they can be photographed.

Optical illusions, on the other hand, are perceptual quirks of human vision, in which the observer sees something that does not exist physically. Of course, the distorted images produced by mirages may elicit optical illusions, when an observer misinterprets the scene ¡ª hence, the confusion of these distinctly different classes of phenomena. (For many examples of optical illusions, please see the Web pages of Akiyoshi Kitaoka, a perceptual psychologist in Japan.)

In a mirage, there is at least one inverted image of some object. This 'mirror image' is the origin of the French word mirage, which s from the phrase se mirer, 'to be reflected; to see one's image in a mirror.'

Often, a mirage contains multiple images, alternately erect and inverted. Mirages are classified according to the number and relative positions of these images. The classical mirages are:

Number of images Name Description
2 Inferior mirage Inverted image below erect one
2 Superior mirage Inverted image above erect one
3 3-image mirage Inverted image between erect ones
many Fata Morgana complex alternation of distorted erect and inverted images

In addition, there are the recently-recognized 'mock mirage' and Alfred Wegener's 'late mirage' or Nachspiegelung. As these have a different optical mechanism, I prefer to call them pseudomirages. Because refraction displaces images primarily in a vertical plane, the various images are usually stacked up directly on top of one another.

Mirages are distinguished from other refraction phenomena such as looming (visibility of distant objects usually hidden below the apparent horizon), towering (exaggerated vertical size of images), sinking (disappearance below the horizon of objects usually seen), and stooping (images squashed together vertically), in which an object may appear distorted, but not inverted. Some of these are milder versions of the phenomena that produce mirages.

Common misconceptions
It is incorrect to say (as even some textbooks do) that a mirage is an image in the wrong place, because atmospheric refraction displaces almost everything we see from its geometric position ¡ª that is, rays of light in the lower atmosphere are usually curved, because the density of air usually decreases steadily with increasing height. Thus, everything normally appears displaced slightly above its geometric or 'true' position. This displacement is known as terrestrial refraction when the object is inside the atmosphere, and astronomical refraction when it is beyond the atmosphere. While these effects are usually small enough to escape casual observation with the naked eye, they are very severe problems in fields such as geodesy and positional astronomy, because they can be hundreds or even thousands of times larger than measurement errors.

Sometimes people think that the erect image of a classical mirage is 'the object itself,' and that the inverted one is 'just a mirage,' and somehow not real. But this notion is challenged by 3-image (and other multiple-image) mirages, in which two or more erect images occur: which one, then, do you choose as 'the real one'? In fact, all the images are equally genuine; every one of them is as truly 'the object itself' as any other, including the inverted ones. And as all the images are in general displaced from the geometric position of the object, location is no indicator of legitimacy.

Indeed, from the point of view of geometrical optics, it is the inverted images that are 'real images.' And the erect images are merely 'virtual images' to an opticist ¡ª including the ordinary appearance of objects, even without mirage conditions! So it is best to recognize that we are really seeing 'the object itself' in every image, even when there are many of them ¡ª while bearing in mind that everything we see is slightly displaced from its 'true' or geometric position by atmospheric refraction, whether there is a mirage or not.

Another common misconception is that the miraged image can fill a large part of the sky, as in this old drawing. Hogwash! Mirages NEVER look like that! They're always confined to a narrow strip of sky at the horizon.

Green flashes and mirages
Green flashes are colored phenomena due to the dispersion of atmospheric refraction. While every refraction phenomenon has some dispersion connected with it, the dispersion is inappreciable under most circumstances. However, certain mirages produce much larger dispersion effects; and the most spectacular of these are the green flashes. So, to understand green flashes, it is first necessary to understand mirages.

It's much easier to understand mirages after you have seen some. Fortunately, the Finnish photographer Pekka Parviainen has made a fine selection of his mirage photographs available on the Web. Take look at them if you are unfamiliar with mirages. Furthermore, Pekka now has his own site, with even more mirage pictures.

A 'textbook example' of a superior mirage was taken by Wim van Bochoven in late May, 2002. He has made his pictures available to me; here they are, with a description of the details. His sequence shows many characteristic features very clearly.

Another site with some good images is Olaf Squarra's pages. He shows a fine multiple-image mirage of the Vestmannaeyjar Islands as seen from Eyrarbakki, on the southern coast of Iceland. There is also a Fata-Morgana type of mirage of farm buildings, shown at the right side of his page; be sure to look at the enlargement.

Some very nice multiple-image mirages, perhaps complex enough to count as Fata Morgana displays, were taken at the Weather Service office in Rapid City, South Dakota, at sunrise on Dec. 19, 2000. Evidently the nocturnal radiative inversion is responsible for this display.

Another fine set of mirage images, photographed through a telescope, is shown on the website of an Australian radio operator, who uses the associated ducts for long-distance radio communication. (See his other pages for the radio logs.) Sample his list of 'Inversion Images' to see a wealth of detail.

Ctein has a very fine inferior-mirage picture that shows many features of these mirages very distinctly. The mirage begins at a sharply defined boundary where the line of sight meets the smooth desert floor at the critical angle; the mirage image is rather irregular near this foreground boundary (because the 'reflection' occurs so close to the ground surface at first that every little irregularity in the surface produces a corresponding wiggle in the reflected image), but with increasing distance behind the boundary, the image bes smoother (as the turning point of the rays moves upward in the air, and so bes less sensitive to small deviations from flatness in the ground). The mirage begins close enough to the camera (only a kilometer or two away) that there isn't much atmospheric scattering in between, so the colors in the erect and inverted images are clear and distinct, and you can see how the inverted images have the same color and brightness as the erect ones ¡ª while the background is a bluish-gray because of intervening airlight. The turbulence produced by the convection currents rising from the hot ground surface makes many lines that should be straight in the picture appear ragged and irregular. Nice.

Another example came from Corindi Beach on the eastern coast of Australia. [The original link is no longer available, but the Wayback Machine provides a copy.] The observer, David James, provided a link to a [now also archived] map that shows where the pictures were taken; he says he was standing at the point where the arrow on the map meets the sea, about 7.2 meters above the sea. (Normal refraction would put his horizon about 10 or 11 km away; however, with the stronger refraction indicated by the mirage, it must be farther away.) The small island that is clearly visible to the right of the mirage in his wide angle shots is North West Solitary Island, about 7 or 8 km from the camera. The mirage was of North West rock, North Solitary Island and the dot on the map above North West Rock, all 25 km or more away. The pictures were taken between 6:11 and 7:47 a.m.; the temperature was 18#176;C, but rose to 33#176;C later in the day. (Probably this was also about the temperature of the hot air above the inversion.) The day was nearly calm ¡ª typical of conditions that produce strong inversions, and superior mirages. The date was 26 September 2003, which is early spring in the Southern Hemisphere ¡ª again, typical season for mirages in temperate latitudes. The nearby islands that are seen undistorted lie a little inside the observer's horizon; the miraged objects are beyond it. Pretty much a textbook example, I'd say. Thanks for the details, David!

Also, there's a nice picture of superior mirages in Alaska here, with a clear explanation of how they're formed.

Atmospheric refraction
Mirages are phenomena of atmospheric refraction; so to understand mirages, you first have to understand refraction in the atmosphere. (I've added a page that emphasizes some basic principles of atmospheric refraction; I hope it will serve as a sort of road map that will keep you from getting lost in all the details.)

Because atmospheric refraction is ordinarily quite small ¡ª usually only a fraction of a degree ¡ª these effects are not ordinarily visible to the naked eye. However, they are easily measurable with optical instruments, and so large that astronomers adjust the mountings of their telescopes to minimize the inconvenient effects of atmospheric refraction.

The air near sea level is about a thousand times less dense than water; but that's still enough to change the direction of light rays that enter it from a different medium, such as the nearly empty space outside our atmosphere. And, because the density of the air changes continuously with height above the Earth, light rays within the Earth's atmosphere bend continuously as they pass from one level to another. Usually, the density decreases steadily from the ground up, so the rays (which always bend toward the denser material) are concave toward the surface of the Earth.

Standard Refraction
Here's a picture of a few nearly-horizontal rays as they pass through the lowest 9 kilometers of air. The label at the outer (right) end of each ray gives its angular altitude above the horizontal (in minutes of arc) at the observer's eye, which is at the vertex of the fan of rays, near the base of the scale of heights at the left. (The diagram is compressed horizontally to magnify small angles above and below the horizontal; 'Hobs' denotes the height of the observer.)