Now, to apply this explanation to the production of the rainbow, which is usually seen under the following circumstances:—The observer is placed with his back to the sun, and at some distance before him rain is falling,—the air between the sun and the rain being tolerably clear. He then often sees two circular arcs or bows immediately in front of him. The colours of the inner bow are the
more striking and vivid of the two. Each exhibits the same series of colours as in the spectrum formed by the prism; namely, red, orange, yellow, green, blue, indigo, and violet; but the arrangement of these colours is different in the two bows, for while in the inner bow the lower edge is violet and the upper red, in the outer bow the lower edge is red and the upper violet. The production of both bows is due to the refraction and reflexion of light, the drops of rain forming, in fact, the prism which decomposes the white light of the sun. The colours in the rainbow have the same proportional breadth as the spaces in the prismatic spectrum. “The bow is, therefore,” as Sir D. Brewster remarks, “only an infinite number of prismatic spectra, arranged in the circumference of a circle; and it would be easy, by a circular arrangement of prisms, or by covering up all the central part of a large lens, to produce a small arch of exactly the same colours. All we require, therefore, to form a rainbow, is a great number of transparent bodies capable of forming a great number of prismatic spectra from the light of the sun.”
The manner in which the drops of rain act as prisms, may, perhaps, be better understood with
the assistance of the following diagram. Suppose the two lower circles to represent drops of rain which assist in forming the primary bow, and the two upper circles similar drops which help to produce the secondary bow; and let S represent rays of the sun falling upon them. The rays of the sun fall upon every part of the drop; but, as those
which pass through or near the centre come out on the opposite side and form a focus, they need not be taken into account. Those rays, however, which fall on the upper side of the drops, will be bent or refracted, the red rays least, and the violet most; and will fall upon the back of the drop in such a manner as to be reflected to the under part of the drop; on quitting which they will be again refracted, so as to be seen at E, where there will appear to the observer a prismatic spectrum with the red uppermost, and the violet undermost. These remarks apply to those drops only which form the upper part of the bow, but it is obvious that a similar reasoning applied to the drops to the right and left of the observer, will complete the
bow. The inclination of the red ray and the violet ray to the sun’s rays, is 42° 2′ for the red, and 40° 17′ for the violet, so that the breadth of the primary bow is 1° 45′.
Thus it will be seen, that the primary bow is produced by two refractions, and one intermediate reflection of the rays that fall on the upper sides of the drops of rain. It is different with the rays which enter the drops below. The red and violet rays will be bent or refracted in different directions; and, after being twice reflected, will be again bent towards the eye of the observer at E; but in this case the violet forms the upper part, and the red the under part of the spectrum. The inclination of these rays to the sun’s rays at S, is 50° 58′ for the red ray, and 54° 10′ for the violet ray; so that the breadth of the bow is 3° 10′, and the distance between the primary and secondary bows is
8° 15′. Hence the secondary is formed in the outside of the primary bow, with its colours reversed, in consequence of their being produced by two reflexions and two refractions. The colours of the secondary bow are much fainter than those of the primary, because they undergo two reflexions instead of one.
There is something very wonderful in the rapidity and perfection with which these natural prisms, the falling drops of rain, produce these effects. In the inconceivably short space of time occupied by a drop falling through those parts of the sky which form the proper angles with the sun’s rays and the eye of the observer, the light enters the surface of the drop, undergoes within it one or two reflexions, two refractions and decompositions, and has reached the eye; and all this is done in a portion of time too small for the drop to have fallen through a space which we have the means of measuring.
It will be understood, that since the eyes of different observers cannot be in precisely the same place at the same time, no two observers can see the same rainbow; that is to say, the bow produced by one set of drops to the eye of one observer is