REPOllT ON PHYSICAL OPTICS. 399 



Let us now inquire what account the wave-theory furnishes 

 of the same phenomena. — A ray of light on entering a crystal- 

 line plate is divided into two, or, in the language of the wave- 

 theory, a series of waves incident upon the crystal is resolved 

 into two within it, which traverse it in different directions and 

 with different velocities. One of these sets of waves, therefore, 

 will lag behind the other, and they will be in different phases of 

 vibration at emergence. When the plate is thin, the emergent 

 waves are superposed ; and as the retardation will then amount 

 only to a few undulations and parts of an undulation, it woiald 

 appear that we have here all the conditions necessary for their 

 interference, and the consequent production of colour. Such 

 was the sagacious conjecture of Young. And indeed, shortly 

 after the publication of the first researches of M. Biot on the 

 laws of the tint3 for different thicknesses, it was observed by 

 Young that these tints corresponded accurately to the interval 

 of retardation of the two pencils ; so that they were manifestly 

 due to interference *. This correspondence is now made out 

 in the fullest manner. It is an easy consequence of Fresnel's 

 theory of double refraction, that the interval of retardation of 

 the two pencils, in traversing a crystalline plate, is nearly pro- 

 portional to the length of their path within the crystal multi- 

 plied by the product of the sines of the angles which its direction 

 makes with the two optic axes ; and as this has been found to 

 be the general measure of the tint, it follows that the forms 

 of the isochromatic curves, — the lemniscates and the circles, — 

 are all necessary consequences of the wave-theory. 



But in the first application of the principle of interference to 

 the colours of crystalline plates there arose a difficulty to which 

 the known laws afforded no answer. So far as this explanation 

 went, the phenomena of interference and of colour should be 

 produced by the crystal alone, and in common light, without 

 either polarizing plate or analysing plate. Such, however, is not 

 the fact ; and the real difficulty seemed to be, not to explain 

 how the phenomena are produced, but to show why they are 

 not ahvays produced. It occurred to MM. Arago and Fresnel 

 to inquire how far the state of polarization of the two pencils 

 might modify the known laws of interference ; and the results 

 of this inquiry t have happily furnished an account of the dif- 

 ficulty, and completed the solution of the problem. It was 

 found that two rays of light polarized in the same plane, inter- 



• Quarterly Review, vol. xi. 



t " Memoire sur 1' Action que les Rayons de la Lumiere polarisce exercent 

 les uns sur les auties," Annales de Chitnie, torn. x. 



