Rainbow

RAINBOW, formerly known as the iris, the coloured rings seen in the heavens when the light from the sun or moon shines on falling rain; on a smaller scale they may be observed when sunshine falls on the spray of a waterfall or fountain. The bows assume the form of concentric circular arcs, having their com mon centre on the line joining the eye of the observer to the sun. Generally only one bow is clearly seen; this is known as the primary rainbow; it has an angular radius of about 42°, and ex hibits a fine display of the colours of the spectrum, being red on the outside and violet on the inside. Sometimes an outer bow, the secondary rainbow, is observed; this is much fainter than the primary bow, and it exhibits the same play of colours, with the important distinction that the order is reversed, the red being in side and the violet outside. Its angular radius is about Among the Greeks and Romans various speculations as to the cause of the bow were indulged in; Aristotle, in his Meteors, erro neously ascribes it to the reflection of the sun's rays by the rain; Seneca adopted the same view. The introduction of the idea that the phenomenon was caused by refraction is to be assigned to Vitellio.

The most valuable of all the earlier contributions to the scien tific explanation of rainbows is undoubtedly a treatise by Marco Antonio de Dominis (1566-1624), archbishop of Spalato. This work, De radiis visus et lucis in vitris perspectivis et iride, pub lished at Venice in 1611 by J. Bartolus, although written some twenty years previously, contains a chapter entitled "Vera iridis tota generatio explicatur," in which it is shown how the primary bow is formed by two refractions and one reflection, and the secondary bow by two refractions and two reflections. Descartes strengthened these views, both by experiments and geometrical investigations, in his Meteors (Leyden, 1637). Descartes could advance no satisfactory explanation of the chromatic displays; this was effected by Sir Isaac Newton. (See Newton's Opticks, book i.

part 2, prop. 9.) The geometrical theory, which formed the basis of the investi gations of Descartes and Newton, afforded no explanation of the supernumerary bows, and about a century elapsed before an explanation was forthcoming. This was given by Thomas Young, who, in the Bakerian lecture delivered before the Royal Society on the 24th of November 1803, applied his principle of the inter ference of light to this phenomenon. His not wholly satisfactory explanation was mathematically examined in 1835 by Richard Potter (Camb. Phil. Trans., 1838, 6, Iv), who, while improving the theory, left a more complete solution to be made in 1838 by Sir George Biddell Airy (Camb. Phil. Trans., 1838, 6, 379).

Geometrical Theory.

The geometrical theory first requires a consideration of the path of a ray of light falling upon a trans parent sphere. Of the total amount of light falling on such a sphere, part is reflected or scattered at the incident surface, so rendering the drop visible, while a part will enter the drop. Con fining our attention to a ray entering in a principal plane, we will determine its deviation, i.e., the angle between its directions of incidence and emergence, after one, two, three or more internal reflections. Let EA be a ray incident at an angle i (fig. I) ; let AD be the refracted ray, and r the angle of refraction. Then the deviation experienced by the ray at A is i-r. If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle ADB equals 2r, i.e., the deviation of the ray at D is 7r-2r. At B, where the ray leaves the drop, the deviation is the same as at A, viz., i-r. The total deviation of the ray is consequently given by D = 2 (i-r)d-r -2r.

Similarly it may be shown that each in ternal reflection introduces a supplemen tary deviation of 7r-2r; hence, if the ray be reflected n times, the total deviation will be D = 2 (i-r)+n(r-2r).