atmospheric refraction

a term applied generally to the refraction of light rays in the atmosphere. Such refraction can result in the apparent displacement of a remote object and, sometimes, in an apparent change in the object’s shape. Some atmospheric-refraction effects—such as the flattened shape of the solar and lunar disks near the horizon, the twinkling of stars, and the shimmering of distant terrestrial objects on a hot day—were known in antiquity. Ptolemy in the second century B.C. knew also of the fundamental refraction effect wherein celestial bodies are seen somewhat above their true positions. The first table of refractions was compiled by Tycho Brahe in the 16th century. An attempt at a theory of refraction was published by J. Kepler in 1604. Not until 1694, however, was a rigorous theory of refraction developed; this was the work of I. Newton.

Because the atmosphere is an optically inhomogeneous medium, light rays propagate in it along curved paths rather than rectilinearly. An object is thus not seen by an observer in its true position. Instead, the observer sees the object in an apparent position located on the tangent at the observation point to the path of the ray. A distinction is made between astronomical refraction and geodetic refraction, or terrestrial refraction. Astronomical refraction is the refraction of rays traveling from a celestial body to an observer. Geodetic refraction, on the other hand, is the refraction of rays traveling from objects located in the atmosphere.

Figure 1

In the case of astronomical refraction, a ray traveling from a celestial body passes through the entire atmosphere. Since the air density and, consequently, the refractive index in general increase along the path of the ray, the path is always convex toward the zenith (see Figure 1). The tangent AS^ʹ to the path passes above the direction AS to the true position of the body. The difference r between the true zenith distance z and the apparent zenith distance z^ʹ is called the refraction error, or simply the refraction. The refraction is equal to zero at the zenith and increases with increasing zenith distance. The simplest theory of refraction does not allow for the curvature of atmospheric layers of equal density and yields the formula

where the coefficient 60ʺ.2 is the refraction constant, B is the atmospheric pressure in mm Hg, and t is the air temperature in °C. The formula can be used for bodies with z < 70°. Exact calculations must take into consideration the effect on the magnitude of the refraction of not only temperature and pressure but also of air humidity and other meteorological factors in the lower atmosphere. Special tables are used for this purpose.

Exact theories of refraction that take into account the sphericity of the earth and the atmospheric layers yield values of refraction at the horizon in excess of 35ʹ (see Table 1).

Near the horizon, r increases with increasing z so rapidly that the lower edge of the solar and lunar disks appears raised a few minutes of arc more than the upper edge. As a result, the disk has a flattened shape. Because of refraction, any celestial body, including the sun, appears above the horizon before it actually

rises and remains visible for some time after it actually sets. Because fast turbulent movements of air masses of different density give rise to continuous fluctuations in the value of the refraction, the images of stars in telescopes shimmer or appear as wobbling, blurred spots of light. The naked eye perceives this effect as the twinkling of stars. This phenomenon severely complicates observations of celestial bodies and necessitates the selection of sites with appropriate atmospheric conditions for astronomical observatories.

Because of the difference in refraction for rays of different wavelengths, which is especially great near the horizon, a colored fringe (blue-green above, red below) and the green-flash effect may be observed at the rim of the rising or setting sun; the image of a star may appear as a vertical spectrum up to 40” in length. For relatively close celestial bodies, such as the moon or artificial satellites of the earth, the value of the refraction differs from that calculated for stars located at the same zenith distance; this effect is called refraction parallax.

The phenomenon of atmospheric refraction is complicated by the inclination of layers of air of equal density to the horizon. This gives rise to horizontal refraction, in which the object is displaced not only in elevation but also in azimuth, albeit slightly. Knowledge of atmospheric refraction is of great importance in astrometry. Because the positions of celestial bodies as determined from astronomical observations are always distorted by refraction in the atmosphere, appropriate corrections must be introduced.

Of the other astronomical phenomena associated with refraction, the illumination of the moon’s disk with reddish light during total lunar eclipses is of interest. This illumination is produced by the sun’s rays that pass through the lower layers of the atmosphere. Because of refraction, the rays are deflected by an angle of up to 70ʹ and illuminate the entire cross section of the earth’s umbra at the distance of the moon. Refraction in the atmospheres of other planets is observed when stars are occulted by the disk of the planet; when this occurs, the star appears in a slightly displaced position. A striking form of refraction is observed in the atmosphere of the planet Venus during transits of the sun. When the planet crosses the sun’s limb, the refracted rays of the sun form a bright ring of light around the part of the planetary disk located outside the sun. This phenomenon was first described by M. V. Lomonosov in 1761.

Radio waves also undergo refraction on passing through layers of the atmosphere having different dielectric constants or different degrees of ionization. The refraction of radio waves in the ionosphere is responsible for the propagation of shortwaves over great distances.