136 KEPOET ON PHYSICAL OPTICS. 



In the prosecution of their researches on the laws of interference 

 of polarized light, MM. Fresnel and Arago discovered further that 

 two oppositely polarized rajs will not interfere, even when their 

 planes of polarization are brought to coincidence, unless they belong 

 to a pencil the whole of which was originally polarized in one 

 plane ; and that, in the interference of rays which have under- 

 gone double refraction, half an undulation must be supposed to be 

 lost or gained, in passing from the ordinary to the extraordinary 

 system. The latter principle is a beautiful and simple consequence 

 of the theory of transversal vibrations. When a vibration in any 

 given direction is resolved into two at right angles, and each of 

 these again into a second pair, in two fixed directions which are 

 also perpendicular, it will easily appear that, of the four com- 

 ponents into which the original vibration is thus resolved, the two 

 in one of the final directions conspire, while those in the other are 

 opposed. The tint produced by the interference of the former, 

 therefore, corresponds to the actual difference of routes of the two 

 polarized rays in the plate ; while that arising from the latter is 

 that due to the same difference augmented or diminished by half 

 an undulation. 



The former of the two laws now mentioned explains the office of 

 the polarizing plate in these phenomena. To account mechanically 

 for the fact of the non-interference of the two pencils, when the 

 light incident upon the crystal is unpolarized, it is necessary to 

 consider such light as a rapid succession of systems of waves 

 polarized in all azimuths ; so that if any two planes be assumed 

 at right angles, there will be an equal quantity of light actually 

 polarized in each. Each of these portions, when resolved into two 

 within the crystal, and these afterwards reduced to the same plane 

 of polarization by the analyzing plate, wiU exhibit the phenomena 

 of interference. But the interval of retardation differs by half a 

 wave in the two cases ; the tints produced therefore will be com- 

 plementary, and the light resulting from their union will be of a 

 uniform whiteness. 



We are obliged to admit, therefore, that common light consists 

 of a rapid succession of systems of waves, in each of which the 

 vibrations are different. But the phenomena of interference 

 (which are exhibited by common light) compel us also to admit, 

 as Professor Airy has observed,* that the vibrations do not change 



* Mathematical Tracts, p. 407. 



