204: THE RAINBOW 



resembles the ridge of a hill, or a watershed, 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 raindrop would be represented by the steepness of 

 the slope. On the top of the watershed that is to 

 say, in the neighbourhood 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 raindrop, 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.* 

 Let me here point to a series of measurements which 

 will illustrate the gradual augmentation of the deflec- 

 tion just referred to until it reaches its maximum, and 

 its gradual diminution at the other side of the maxi- 

 mum. The measures correspond to a series of angles 

 of incidence which augment by steps of ten degrees. 



* 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 as the convergence is not quite 

 exact, the parallelism after emergence is only approximate. The 

 emergent rays cut each other at extremely sharp angles, thus 

 forming a "caustic" which has for its asymptote the ray of 

 maximum deviation. In the secondary bow we have to deal with 

 a minimum, instead of a maximum, the crossing of the incident 

 and emergent rays producing the observed reversal of the colours. 

 (See Engel and Shellbach's published diagrams of the rainbow.) 



