Atmospheric Optics Glossary

This doesn't pretend to be complete. It does try to explain technical terms used in my green-flash/mirage/refraction pages. These terms are drawn from a variety of disciplines: optics, meteorology, astronomy, hydrography, navigation, geodesy, etc.

Links in italics  refer to other terms in this Glossary. Links in boldface refer to the bibliography.

If you can't find a term here, try the alphabetical index. If you still can't find it, please write to me and ask that the missing term(s) be added.

Also, remember that many technical terms are briefly defined in most unabridged dictionaries; the 1913 Webster's on the Web has some. I think the new, second edition of the Glossary of Meteorology, published in 2000, and now available at, is pretty reliable.

There are several glossaries of astronomical terms available, which you may find useful to supplement this list:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z


AEROSOL refers to small particles suspended in the air, as opposed to big “hydrometeors” like snowflakes and raindrops. Aerosols make the air look hazy by scattering light; the loss of light by scattering increases the atmospheric extinction.

The relative AIRMASS is the ratio of the amount of air in the line of sight (at some zenith distance Z) to the amount in the zenith. It gives the relative amounts of molecular extinction at different zenith distances.

ALTITUDE: Angular distance above (positive) or below (negative) the horizontal (i.e., the astronomical horizon.) Altitude is usually measured in degrees and minutes of arc.

This is the astronomical definition of the term. In common usage, “altitude”, “elevation”, “height” and the like are used indiscriminately for both angular and linear measurements; and the technical usage varies from one field to another. Be aware of possible confusion here.

Because altitude is the coordinate affected by refraction, it's usual to distinguish between apparent  altitude (the observed quantity, affected by atmospheric refraction) and true or geometric  altitude (where an object would appear without the effect of refraction).

APPARENT HORIZON: Where the sky appears to meet the Earth. (See also sea horizon.) Because of perspective effects, different observers generally have different apparent horizons. Because of refraction, even the sea horizon usually lies above the geometric horizon.

ASTRONOMICAL HORIZON: the intersection of a horizontal plane through the eye with the celestial sphere. (NOTE: because the celestial sphere has an infinite  radius, two observers at different heights above sea level, but placed on the same vertical line, have the same astronomical horizon.) Because of dip, the astronomical horizon always lies above the sea horizon. But it usually is hidden by trees, hills, and buildings on land. These objects then determine the observer's apparent horizon (see above).

ASTRONOMICAL REFRACTION: The displacements of astronomical objects by atmospheric refraction. Near sea level, the effect is about a minute of arc at 45° from the zenith, and increases roughly with the tangent of the zenith distance; at the horizon, it is typically about half a degree, and quite variable. These effects are many orders of magnitude larger than the accuracy of the best astronomical position measurements, and so large that the mountings of most astronomical telescopes are adjusted to minimize the effects of refraction. See also terrestrial refraction.


BOUNDARY LAYER: A relatively thin layer of fluid next to a boundary (such as a solid or liquid surface). Example: the layer of air next to the Earth's surface (the “planetary boundary layer”). Ordinarily, only the boundary layer is appreciably affected by the properties of the surface. The rest of the fluid is unaffected; so the part of the atmosphere above the boundary layer (which is typically a few hundred meters thick) is called the “free atmosphere.”

BOUNDARY LAYER METEOROLOGY is the name of the discipline that studies atmospheric boundary layers, as well as the name of a leading journal in this field.


CELESTIAL SPHERE: An imaginary sphere of infinite radius, centered at the observer. A point on the celestial sphere is really only a direction in space; parallel lines meet the celestial sphere in the same point.

CREPUSCULAR RAYS: When the lower atmosphere is hazy, light passing through gaps between broken clouds can produce bright “beams” that are made visible by scattering by aerosol particles. These are usually seen best when the Sun is low, or at twilight (hence the term “crepuscular.”)


DENSITY: How much stuff there is in how much space. The density of water is 1 gram per cubic centimeter, or one (metric) ton per cubic meter. The density of air is about 1 kilogram per cubic meter — about a thousand times less dense than water. The density of air is proportional to its pressure, and inversely proportional to its (absolute) temperature.

DIP: The dip of the apparent (or sea) horizon is its angular distance below the astronomical horizon. See the dip page for details.

DISPERSION: The variation of refraction, or refractive index, with the wavelength or color of light. All transparent media — air, water, glass, etc. — are dispersive. Normally, the refraction is greater for the short wavelengths (blue and violet) and least for the long ones (red light). See my dispersion page for details.

DUCT: If the ray curvature within a thermal inversion is stronger than the curvature of the Earth's surface, rays can be continuously guided near the surface of the Earth without ever escaping to space. This region in which rays are trapped is called a duct. An observer within the duct sees a superior mirage of distant objects within the duct. Ducting occurs when the temperature gradient within the inversion is steeper than about 10 K in 100 meters (1 degree in 10 m). See the duct page for details.


EXTINCTION: loss of light in the atmosphere. Extinction is the sum of actual absorption, and scattering.


FATA MORGANA: A complex mirage display that involves multiple images, alternately expanded and compressed vertically, often giving the impression of buildings, cliffs, etc. where no such objects exist. The name is traditionally used in Italy for the vivid mirages seen across the Strait of Messina. (See my Fata Morgana page for details.)


GEODESY is the study of the size and shape of the Earth. The corresponding adjective is geodetic .

GEOID is the equipotential surface corresponding to mean sea level. NOAA has a nice discussion of this term.

GEOMETRIC HORIZON: Where the apparent sea horizon would be if there were no refraction; equivalently, where the cone with vertex at the observer's eye and tangent to the sea surface would meet the celestial sphere.

GRADIENT: the rate at which something changes; here, we are talking about temperature gradients: how fast the temperature changes with height in the atmosphere. The bending of rays in the atmosphere depends on the temperature gradient.

GREEN FLASHes are phenomena seen at sunrise and sunset, when some part of the Sun suddenly changes color (at sunset, from red or orange to green or blue). There are several quite different phenomena commonly lumped together under the name of “the green flash”, and this intermingling of disparate phenomena has fostered confusion. So I prefer to say “green flashes” and avoid the definite article. [See the photographs and simulations.]

GREEN RAY: a rare kind of green flash, in which an actual beam of green light is seen shooting up from the horizon where the Sun has just set, or from the Sun itself. Usually this beam or ray is only a few times larger than the Sun itself; sometimes, it appears as a diffuse glow. I now have a separate page on this topic. Unfortunately, the term “green ray” has often been used for green flashes in general — a confusing practice that should be discouraged.

GREEN RIM: When the Sun is low, normal atmospheric dispersion raises the short-wavelength images of the Sun more than the long-wavelength images; but atmospheric extinction attenuates the blue so much that the upper edge usually appears green, not blue or violet. See the simulation of a sunset in the Standard Atmosphere. The green rim is so narrow that it can only be seen telescopically.

GREEN SEGMENT: Mulder's term (popularized by his followers Minnaert and O'Connell) for all the common kinds of green flash together. This catch-all category is no longer useful, and should be avoided.


HEIGHT: Linear distance (usually measured in meters) above sea level; as contrasted with altitude, which is angular distance above the astronomical horizon. Usually called “elevation” by geographers.

HORIZON: An ill-defined term, used in many ways: see apparent horizon, astronomical horizon, and geometric horizon. To an astronomer, one of these horizons is a collection of directions in space, and in fact a circle on the celestial sphere. To most other people, “horizon” means the visible edge of some physical object; then it makes sense to speak of the “distance to the horizon,” a usage that seems absurd astronomically.

HORIZONTAL REFRACTION: The astronomical refraction at the astronomical horizonnot  refraction parallel to the horizon, as non-astronomers might suppose.


ILLUMINANCE: The amount of visible light per unit area. This is the visual quantity analogous to the radiometric quantity irradiance.

INDEX OF REFRACTION: See refraction.

INFERIOR MIRAGE: "Inferior" means "lower"; this is the mirage in which the inverted image is below  the normal one. The common example is the hot-road mirage seen on sunny days.

INVERSION refers to something being upside down. Don't confuse inversion of an image with inversion of the temperature gradient (a thermal inversion).

IRRADIANCE: The amount of power per unit area in a beam of light. Sometimes also called flux . Units: W m-2




LAPSE RATE: The rate at which temperature de creases with height in the atmosphere. This has the opposite sign from the temperature gradient a physicist would use, so be careful.

LATERAL MIRAGE: A much mis-used term. Refraction in the horizontal direction is appreciable only when a boundary layer is stabilized by a wall or other near-vertical surface; in such cases, the term “mural mirage” is more descriptive. (See here for further discussion.)

Unfortunately, the existence of the term “lateral mirage” has encouraged uncritical observers to think they have seen images separated by many degrees in azimuth from the actual direction to the object. These are always cases of mis-identification; atmospheric refraction cannot produce such effects.

LOOMING: The appearance above the horizon of a distant object that would normally be hidden below it. This effect is caused by unusually large terrestrial refraction, usually due to a thermal inversion. Looming is the opposite of sinking. Both are refraction phenomena, but not mirages. (See the table of refraction phenomena, and the simulations.)

LUMINANCE: The amount of visible light per unit area and per unit solid angle. Often called “surface brightness”. This is the visual quantity analogous to the radiometric quantity radiance.


MINUTE: Don't confuse a minute of time with a minute of arc. A minute of time is 1/60 of an hour; a minute of arc is 1/60 of a degree.

MIRAGE: An inverted image caused by atmospheric refraction.

I'm surprised to find mirages defined in very different ways in various reference books and dictionaries. Some are too restrictive, and/or give incorrect explanations. Others run to the opposite extreme, with definitions so broad as to include almost everything you see.

I consider a mirage to be any display of atmospheric refraction that produces either multiple images of an object, or at least one inverted image. (It can be shown that these descriptions are essentially equivalent; however, in practice, one or more of the multiple images may be so compressed or distorted as to be unrecognizable.) There are many kinds, including the classical inferior and superior mirages, the mock mirage, and Wegener's Nachspiegelung. I have a mirage page where these phenomena are explained more fully. (Also, see the table of refraction phenomena.)

MOCK MIRAGE: an inverted image produced by a thermal inversion below eye level. (See the ray diagram on the mirage page for details.) While the classical inferior and superior mirages can be regarded, for some purposes, as due to internal reflections, no such interpretation is possible for the others, which might well be called “pseudo-mirages.”

Caution: terms like “mock mirage” and “pseudo-mirage” should not be taken to mean that these phenomena are any less real than the classical inferior and superior mirages. The names are chosen simply to distinguish the recently-understood mirages from the classical ones, which involve different optical mechanisms. See the ray diagrams on the mirage page for an explanation of the common kinds, and the table of refraction phenomena.

MURAL MIRAGE: A mirage produced by the boundary layer of hot air next to a heated or sunlit wall. It is essentially an inferior mirage turned on its side. See here for further discussion.


NACHSPIEGELUNG: Alfred Wegener's term for the “late mirage” seen by an observer within a duct after  the Sun has passed the “reflecting” or “obscured” strip (i.e., the superior mirage) produced by a duct. See the ray diagram on the mirage page, and the table of refraction phenomena.


OPTICAL DEPTH: If the transmission of a slab of material is   t = exp(-τ)   then we say that τ is the optical depth of the material. So the optical depth is the negative of the natural logarithm of the transmission. (Note that it is a dimensionless number.)

A similar measure of opacity, called optical density , which is used in photography, uses the common (base 10) logarithm instead of the natural (base e ) one. Don't confuse them.

ORIANI'S THEOREM: A proof that astronomical refraction is independent of atmospheric structure above the observer, from the zenith to about 70° zenith distance.


PERIGEE: The point on a trajectory, or the path of a refracted ray, that is nearest the center of the Earth.

PSEUDO-MIRAGE: A mirage that cannot be explained, even approximately, as due to internal reflection at the interface between warm and cool air. The mock mirage and Wegener's Nachspiegelung are examples of pseudo-mirages.



RADIANCE: The amount of power per unit area and per unit solid angle in a beam of light. (Think of it as the irradiance per unit solid angle.) Units: W m-2 sterad-1

RED FLASH: the less-conspicuous complement of a green flash. There are a few in the list of pictures, and some simulations.

REFRACTION: the bending of rays of light in passing from one medium to another (e.g., air to water), or between parts of the same medium with different densities (e.g., different levels in the atmosphere). The amount of refraction is given by Snel's law, which is expressed in terms of the medium's refractive index, which is just the ratio of the speed of light in a vacuum to that in the medium. (See the refraction page.)

Don't confuse refraction  (the process) with refractive index  (a ratio of propagation speeds), or the latter with refractivity  (which is the refractive index minus unity.) In gases, it is an excellent approximation to set the refractivity proportional to the density of the gas. Things are more complicated for dense materials like solids and liquids, however.

Also, don't confuse re fraction with dif fraction, which is the spreading-out of light at the edge of a shadow. Diffraction is purely a wave-optical phenomenon, and is appreciable only when the lateral dimension of an object in the path of the light is only a few wavelengths. Refraction is a ray-optical phenomenon that strictly is useful only when objects are many wavelengths across. So the two phenomena are usually important only in mutually exclusive situations. But, because the words are similar, many people confuse the two terms.


SCATTERING: When light passes through a medium that is not perfectly homogeneous, the irregularities in the medium scatter some of the light in all directions. Even the molecules of air are large enough to scatter light; in 1871, Lord Rayleigh showed that this accounts for the blue sky. (Since then, molecular scattering has been called “Rayleigh scattering.”)

SEA HORIZON: The apparent horizon formed by the sea.

SINKING: The disappearance below the horizon of distant objects normally visible; the reverse of looming. (See the table of refraction phenomena, and the simulations.)

SNEL'S LAW gives the quantitative change of direction of a ray of light in passing from one medium to another. The product n  sin z  is the same on both sides of a plane interface between two media, where n  is the local refractive index, and z  is the local angle the ray makes with the normal to the interface. (See the refraction page.)

In the curved atmosphere, Snel's law becomes nR  sin z  = constant, where R  is distance from the local center of curvature; see the page especially devoted to this refractive invariant.


U.S. Standard Atmosphere, 1976
U.S. Government Printing Office, Washington, D.C., 1976

but is very similar to its 1962 predecessor, and to the 1958 ICAO Standard Atmosphere in the lower parts that are important for refraction. (Further details are available from NASA, Digital Dutch's calculator, the AMS Glossary, and other sources.) Its most important property, for present purposes, is its constant lapse rate of 6.5 K/km. (I have a page that shows its temperature profile.)

This “model atmosphere” is a highly idealized version of the average of many measurements made in the real atmosphere. Thus, it lacks the fine structure that is always present in the real world.

STOOPING: Vertical compression of the refracted image of a distant object; the opposite of towering. (See the table of refraction phenomena, and the simulations.)

SUPERIOR MIRAGE: "Superior" means "higher"; this is the mirage in which the inverted image is above  the normal one. These are somewhat uncommon, and are associated with ducting.


TERRESTRIAL REFRACTION: The displacement of terrestrial objects from their geometric directions by atmospheric refraction. You may not notice it, but it is a major headache for geodesists and surveyors. Cf. astronomical refraction.

THERMAL INVERSION: On the average, the temperature in the lower atmosphere decreases with increasing height. (The average gradient is about 6.5 K per kilometer.) A region in which the warmer air lies above the colder air is said to have an “inverted” temperature gradient, and is called a “thermal inversion,” or “inversion layer.” A thermal inversion is required to produce a superior mirage.

TOWERING: Abnormal vertical stretching of the image of a distant object; the opposite of stooping. Towering and stooping are refraction phenomena that distort but do not invert images; hence, they are not mirages. (See the table of refraction phenomena, and the simulations.)







ZENITH: The point in the sky straight overhead (i.e., the direction “straight up”). The direction to the zenith is perpendicular to the astronomical horizon.

ZENITH DISTANCE: The angular distance of an object from the zenith. The zenith distance of an object is the complement of its altitude. The zenith distance of the astronomical horizon is 90 degrees.

© 1999 – 2017, 2020 Andrew T. Young