RAINBOW (A.S. Regnboga, reuboqa; OD G. regan-bogo: Ger. Regenbogcn, from Reqen, rail), and boga, bow). The term applied to the are of prismatic colors which at times is seen when the sun or moon is shining while it is raining. It always is seen in the part of the heavens opposite to the sun, and is high when the sun is low, and low, near the horizon, when the sun is high. It is a short are. o• a complete one, resting on the earth at each end. according to the extent of the rain. Sometimes u second concentric how is seen with the colors reversed. Both are due to the reflection and refraction of the rays of the sun in the drops of rain.
If the parallel lines S, Fig. 1. represent rays corning from the sun and falling upon the drop of water, the centre of which is 0, it is possible to determine the path of each ray by applying the simple law of refraction. For example: the ray ST1 will be refracted to A. reflected to C, and finally refracted out to T. The parts of the ray which are reflected out at B, refracted out at A. o• reflected in at C, need not be con sidered, as they do not contribute to the phe nomenon. It may he shown that when the arcs BA and AC are equal, then the angle between SB and CT is greater than for any other case. In other words, when the ray passes tln•ongh the drop symmetrically, the final direction of the ray is at the greatest angle with the original direction. and also that a greater proportion of the total light falling on the drop is sent out in this direction than in any other. The light which falls farther out on the drop than Ti is mostly reflected off the drop, and that which falls nearer than B enters the drop, but mostly passes out at the back at A. Inasmuch as the index of refraction is different for the different colored lights, it follows that the angle between SB and CT must be different for the different colors, less for violet than for red. An eye at T, Fig. 2, looking toward the drop, would see considerable of the light coming in the direction CT, but an eye at would only see a little light corresponding to the ray SB2A,C2T2. and an eye at E, would see no light
from that drop. If we imagine the whole of Fig. 2 revolved upon the line TS' as an axis, them the ray SB becomes a cylindrical shell of rays, the drop becomes a circular arc of drops, and the ray CT becomes a conical shell of rays, which. seen by the eye at T, appears as a ring of light against the clouds as a background, having an angular radius equal to CTS'. if the red rays are considered this radius would be about 42° 22'. and for the violet rays 40° 35', and for the intervening colors it would have corresponding values. Thus the ring of violet would appear the smallest and the red the largest, with the other colors ranged between. Of course, a particular drop is only in the right position to contribute to this ring of light for a small frac tion of a second, hut others take its place. Moreover, the apparent diameter of the sun causes a widening of the line of light to a band, and these bands of different colors overlap and blend. The bow formed as above described is called the 'primary bow' and is much brighter than the 'secondary bow,' which is formed as follows: By a line of reasoning entirely an alogous to that given above, it may be shown that light falling upon the opposite half of the drop. as shown in Fig. 3, may undergo two reflections in the drop and emerge in the direc tion DT. Again, when the path is symmetrical in the drop, the angle between SP, and DT is now smaller than for any other ease, hut larger for violet than for red, and in all eases larger than the angle between SB and CT in the pri mary how. Applying a similar consideration to Fig. 4, and considering it revolved upon the line were calculated by Airy and experimentally veri fied by Miller. When the conditions are very favorable other fainter bows may be seen inside the primary and outside the secondary bow. These correspond to a still more complex com bination of reflections and refractions of the rays in the drops. A lunar rainbow differs from a solar bow only in the intensity of the light and consequent paleness of the colors.