Usually the most conspicuous colour in the principal rainbow is the red; but wide variations are noted from one bow to another not only in the brightness and purity of the different colours, but also in their angular width. This is not in accordance with the elementary theory, which would require all rainbows to be similar in the distribution of colours as well as in their relative intensity. The fuller treatment of the theory which is based on the undulatory theory of light will be found in Pernter-Exner's Meteorologische Optik, or in Humphreys' Physics of the Air. It can be shown that the phenomena depend in a very marked way on the size of the water drops, and that the width of the coloured bands increases as the size of the drop decreases. The elementary theory leads to the result that there is a direction of maximum illumination along the direction of minimum deviation, but the more detailed theory leads to the result that there are other directions along which there is considerable illumination. The subsidiary maxima account for the spurious bows, whose dis tance from the main bow is greater for small drops than for larger drops. The actual primary rainbow observed is thus the effect of the superposition of a number of bows. If the red of the second bow falls upon the green of the first, the result is to give a bow with an abnormally wide yellow band, since red and green lights when mixed form yellow. This is a very common type of bow, one showing mainly red and yellow, with little or no green or blue. If the drops are smaller the red of the second bow may
fall within the blue of the first bow, so that we should then see a second bow (spurious bow) within the first. The phenomena are further complicated by the variation in the size of raindrops within the cloud. Since the smaller drops occur in the upper levels, the spurious bow is generally observable only near the top of the bow.
With very small drops, whose diameter is o.i mm. or less, the colours become superimposed, and the rainbow becomes almost a pure white. This type of rainbow, sometimes known as Ulloa's Ring or as a fog-bow, is only seen distinctly when the observer is very near the cloud which produces it.
The centre of a rainbow is at the same angular distance below the horizon as the sun is above the horizon. Rainbows can be formed by light coming from the reflection of sunlight in a water surface. The observer then sees more than a semicircle of this rainbow, the centre being above the horizon ; and he will at the same time see the rainbow formed in the usual way by direct rays from the sun. The two rainbows intersect, and are commonly referred to as intersecting rainbows.
Rainbows can also be formed by moonlight, but the colours are then very faint, and difficult to distinguish.
The physical theory of rainbows is given in R. W. Wood's Optics; Preston's Theory of Light; Humphreys' Physics of the Air; and Pernter-Exner's Meteorologische Optik. (D. BRU.)
RAINBOW TROUT (Salmo irideus) : see TROUT.