upon the angle between them. In the tropics, where this angle is nearly or quite 90°, the distance below the horizon clearly increases most rapidly, and twilight that fades away with increase in this distance is of short duration. In high latitudes, where the angle in question is not large, the horizon distance of the sun increases less rapidly, and therefore the twilight is of correspondingly longer duration.
Mirage. --It often happens that the air next the surface of a level desert plain becomes strongly heated and so expanded that it is lighter than the layers immediately above it. In this condition it will transmit rays of light at greater speeds than will the overlying denser air. Consequently, a ray of light from a distant elevated object may pass first to this heated stratum and there, by a process of gradual refraction, or, if the two layers are sharply separated, by total reflection, be turned up to the observer's eye, just as is the case in reflection from water, for which such layers of air are often mistaken. Any phenomenon of this general nature is called a mirage.
Irregularities in the unequally refracting (because unequally heated) layers of air produce corresponding irregularities in the resulting phenomena, to some of which are given specific names. The term mirage is commonly restricted to phenomena such as would be seen in a horizontal mirror placed at a level below that of the eye of the observer, while looming is a term restricted to the analogous phenomena that appear to come from reflection in a horizontal mirror at some level above the observer. The term Fata Morgana is a local ( Italy and Sicily) name for any mirage, rather than a specific name restricted to some definite manifestation of the phenomenon.
The only recent extensive general treatise on atmospheric optics is J. M. PERNTER and FELIX M. EXNER'S "Meteorologische Optik," Vienna, 1902-10.
E. MASCART'S "Traité d'optique" ( 3 vols. and atlas), Paris, 1889-94, devotes much space to meteorological optics. See especially vol. iii.
On optical effects of the Krakatoa eruption see:
ROYAL SOCIETY OF LONDON, "The Eruption of Krakatoa, and Subsequent Phenomena," edited by J. G. SYMONS, London, 1888.