220 INTERFERENCE OF POLARIZED LIGHT. 



components into which the original vibration is thus resolved, 

 the pair in one of the final directions must conspire, while in 

 the other they are opposed. Accordingly, if the vibrations of 

 the one pair are coincident, those of the other differ by half an 

 undulation. Hence, when the plane of reflexion of the ana- 

 lyzing plate coincides successively with these two positions, 

 the colours (which result from the interference of the portions 

 in the plane of reflexion) will be complementary. 



The former of the two laws explains the office of the 

 polarizing plate in the phenomena. To account mechani- 

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

 light incident upon the crystal is unpolarized, we may regard 

 a ray of common light as composed of two rays of equal inten- 

 sity, oppositely polarized,* and whose vibrations are therefore 

 perpendicular. Each of these vibrations, when resolved into 

 two within the crystal, and these two again resolved in the 

 plane of reflexion of the analyzing plate, will exhibit the phe- 

 nomena of interference. But the interval of retardation will 

 differ by half a wave in the two cases ; the tints produced will 

 therefore be complementary, and the light resulting from their 

 union will be of a uniform whiteness.! 



* More properly, a ray of common light must be regarded as composed of an 

 indefinite number of rays polarized in all azimuths ; so that if any two planes 

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

 larized in each. Ordinary light, in fact, consists of a series of systems of 

 waves, in each of which the vibrations are different ; the different systems suc- 

 ceeding one another so rapidly, that, in a moderate time, as many vibrations 

 take place in any one plane, as in another at right angles to it. But the phe- 

 nomena of interference, exhibited by common light, compel us also to admit (as Sir 

 G. B. Airy has observed) that the vibrations do not change continually ; and that 

 in each system of waves there are, probably, several hundred vibrations which 

 are all similar, although the vibrations constituting one system bear no rela- 

 tion to those of another, and the different systems succeed one another with such 

 rapidity as to obliterate all trace of polarization. 



f "We have here supposed the resulting light to be simply the sum of the 

 lights derived from each of the portions into which the original light was sup- 



