When sunlight falls on drops of water which are not small compared to the length of a light wave, an entirely different phenomenon, involv ing reflection, refraction and dispersion, results. It can be shown that, when flat wave-surfaces of light enter a sphere of water, there are two cases in which a portion of the wave emerges from the drop still nearly flat, and that in these directions, therefore, the light will be trans mitted with relatively great intensity. The first case corresponds to refractions at entrance and emergence with a single interior reflection; and the second case to the two refractions separated by two interior reflections. The total change of the direction of the light in the former case is 138 degrees and in the latter 231 degrees. It, therefore, follows that all drops at these two angular distances from the sun should appear relatively bright, in other words, that opposite to the sun there should appear two concentric circles under proper conditions of illumination, one, much the brighter of the two, of 42 degrees radius and the other of —51 degrees radius. The secondary phenomenon of dispersion causes these angles to vary continuously for different wave-lengths, hence the circular arcs, constitut ing the double rainbow when perfectly devel oped, appear as bands of prismatic colors. It is not difficult to see that the primary bow, often the only one which can be traced, must be red on the outer border, whence we conclpde from the algebraic sign attached to its radius, that the secondary bow should present the red border on the inner margin.
When the temperature is low, water cannot exist in the form of drops, but only in that of snow crystals and of a perfectly transparent vapor. On those occasions when there are nu merous ice crystals of very regular form sus pended in the air and illuminated by the sun or the moon, we may see one or more of a series of highly complicated phenomena which bear the names of halos, parhelia, sun-dogs, etc. A bare description of all the features which have been observed and recorded would demand far more space than is available; only the most common ones can be noted here. The simplest form of ice crystals, and the only form which is necessary to produce all the known forms of halos, is that of a right hexagonal prism. Such
a body supplies two refracting angles, namely, that of 60 degrees contained between two alter nate faces of The prism, and that of 90 degrees embraced between each of these faces and a base. As light traversing a 60-degree prism of Ice has a minimum deviation of 22 degrees, if there are present a sufficient number of such prisms between the sun or moon and the ob server, the luminous body would seem to be surrounded by a concentric circle of 22 degrees radius, having, on account of the secondary effect of dispersion, a red inner margin and a pale bluish outer one. Similarly the rectangular edges would give rise to a colored circle of 44 degrees radius. The smaller circle can be seen very frequently—perhaps on 60 to 80 days a year in our latitude — while the 44-degree circle is rarely seen.
When the length and width of a small hex agonal prism differ greatly, it will not remain while falling through quiescent air in a purely chance position, but it will set itself more or less perfectly in a definite position with respect to a vertical. Thus a flat prism will fall with its base horizontal, and an elongated crystal will maintain its axis nearly horizontal. This pecu liarity in falling crystals produces a large num ber of features in complicated halos which are generally recognizable.because they are all sym metrical with respect to a vertical circle pass ing through the sun. Some of these are com parable with the most brilliant rainbows in their coloring. The most familiar of this class of phenomena are the two bright prismatic spots to the right and left of the sun, respectively, having the same altitude as the sun and their red side turned toward the sun. When the sun is very low they are 22 degrees distant and appear merely as bright portions of the inner halo, but as the altitude of the sun increases they increase their angular distances, and above a moderate altitude they disappear. These spots are called parhelia, or sun-dogs; they are some times the only feature of the halo visible and are by no means infrequent. See also CAMERA; ELECTRICITY; ELECTRIC LIGHT; MICROSCOPE; POLARIZATION OF LIGHT; TELESCOPE; VISION.