a sheaf of approximately parallel rays. But what determines this parallelism? Here our real difficulties begin, but they are to be surmounted by attention. Let us endeavor to follow the course of the solar rays before and after they impinge upon a spherical drop of water. Take first of all the ray that passes through the center of the drop. This particular ray strikes the back of the drop as a perpendicular, its reflected portion returning along its own course. Take another ray close to this central one and parallel to it—for the sun's rays when they reach the earth are parallel. When this second ray enters the drop it is refracted; on reaching the back of the drop it is there reflected, being a second time refracted on its emergence from the drop. Here the incident and the emergent rays inclose a small angle with each other. Take again a third ray a little farther from the central one than the last. The drop will act upon it as it acted upon its neighbor, the incident and emergent rays inclosing in this instance a larger angle than before. As we retreat farther from the central ray the enlargement of this angle continues up to a certain point, where it reaches a maximum, after which further retreat from the central ray diminishes the angle. Now, a maximum resembles the ridge of a hill, or a water-shed, from which the land falls in a slope at each side. In the case before us the divergence of the rays when they quit the rain-drop would be represented by the steepness of the slope. On the top of the water-shed—that is to say, in the neighborhood of our maximum—is a kind of summit level, where the slope for some distance almost disappears. But the disappearance of the slope indicates, in the case of our rain-drop, the absence of divergence. Hence we find that at our maximum, and close to it, there issues from the drop a sheaf of rays which are nearly, if not quite, parallel to each other. These are the so-called "effective rays" of the rainbow.^{[1]}
Let me here point to a series of measurements which will illustrate the gradual augmentation of the deflection just referred to until it reaches its maximum, and its gradual diminution at the other side of the maximum. The measures correspond to a series of angles of incidence which augment by steps of ten degrees:
i | d | i | d | ||
10° | 10° | 60° | 42°28' | ||
20° | 19°36' | 70° | 39°48' | ||
30° | 28°20' | 80° | 31° 4' | ||
40° | 35°36' | 90° | 15 | ||
50° | 40°40' |
The figures in the column i express these angles, while under d we have in each case the accompanying deviation, or the angle inclosed
- ↑ There is, in fact, a bundle of rays near the maximum, which, when they enter the drop, are converged by refraction almost exactly to the same point at its back. If the convergence were quite exact, then the symmetry of the liquid sphere would cause the rays to quit the drop as they entered it—that is to say, perfectly parallel. But inasmuch