322 Prof. Potter on the Interference of Light near a Caustic, 



Whilst an undergraduate at Cambridge, on studying the 

 theory of the rainbow I found that it belonged to the same class 

 of interferences near a caustic, and was not aware, until informed 

 by Professor Whewell, that Dr. Young had applied the principle 

 of ray interference to explain the occurrence of supernumerary 

 rainbows seen frequently within the primary bow, and some- 

 times exterior to the secondary bow, of which the Newtonian 

 theory of the rainbow furnishes no account. 



In a paper published in vol. vi. p. 140 of the Cambridge 

 Transactions, I have shown the necessity of the doctrine of inter- 

 ference to solve the phenomena, and have traced the caustic for 

 the primary bow. At the time of writing that paper in 1835, 

 1 had not entered into any adequate examination of the point 

 whether the rainbow occurred at or within the caustic, but did 

 so soon afterwards, and I urged that it was found within the 

 caustic in a discussion in the Cambridge Philosophical Society 

 in the spring of 1836. In the Philosophical Magazine for July 

 1838 will be found the calculations on which this conclusion 

 was founded, showing that there was darkness at the place for- 

 merly attributed to the rainbow. 



This has been fully confirmed by M. Bravais* in numerous 

 measures of the radii of fog-bows, which he found to be less 

 than calculated for the rainbow, and to vary from 34° to 42°. 

 Not being aware that the primary rainbow was also within its 

 calculated place, he supposed that fog-bows required the occur- 

 rence of vesicular vapour for their formation. The existence of 

 any such vapour has not, however, been demonstrated, and is 

 generally disbelieved. His arguments from the absence of 

 colour in the fog-bow, or arc-en- del blanc, are not of any weight 

 as to its origin being different from that of the rainbow, for I 

 believe the outer edge is always tinged with red. 



Mr. Airy, the Astronomer Royal, has given an investigation 

 in vol. vi. p. 379 of the Cambridge Transactions, of the intensity 

 of light near a caustic, by employing M. Fresnel s principle, that 

 each point in the front of a wave may be considered as the origin 

 of a new wave, and the intensity at any given point is the result- 

 ing intensity from the surface of the wave in any of its previous 

 positions considered as made up of such origins. This method 

 of discussing interferences, which fails in so many cases when 

 examined with impartial eyes, gave the maximum intensity of 

 the primary bow to be within the caustic, but that the bright- 

 ness was still nearly half the maximum at the place of the caustic, 

 and that the light extended on its outside, shading gradually to 

 darkness at an indefinite distance. 



The measures before referred to were a sufficient guarantee 



* See Repertoire d'Optique Moderne, by the Abbe Moigno, p. 1610. 



