Phenomena of the Rainbow. 



283 



* Let us next consider two refractions separated by one reflexion ; the 

 same construction (see Fig. 2.) and reasoning will apply : only the angle 



Fig. 2. 



I C I" will be double I C I', that is, equal to 2 (180 - 2r) ; thus we 

 have A + 2 i + '2 (180 - 2r) = 2, 180, and A = 4 r - 2i. 



' Generally, if the ray have n successive incidences in the interior of 

 the globe, the angle I C I" becomes n (180 - 2 r). 



' The angular deviation will be constant for all rays of the same 

 nature, which penetrate the globe under the same incidence ; but the 

 incidence changing, that also will change. To form a clear idea of these 

 variations, let us first consider the case in which the ray suffers but one 

 internal reflexion ; after which it escapes from the globule into the air. 

 Then, if we calculate the amount of deviation for several parallel rays, 

 incident at small distances on various parts of the surface, it will be 

 found that the deviation is nothing under a perpendicular incidence, in 

 which the ray passes through the centre of the globule. The deviation 

 gradually increases to a certain limit of incidence, which is about 54 

 for the red rays, so that a pencil of these rays entering parallel at 

 I (see Fig. 3.) under this incidence, and being once reflected from 



Fig. 3. 



the inner surface, will emerge equally parallel at I", though the general 

 direction of the pencil be deviated 42. But for more considerable inci- 

 dences, the deviation diminishes as it had increased ; and this diminution 



