206 UNDULATORY THEORY OF LIGHT. 



this case lost (approximately) au even number of lialf undulations, will comport 

 themselves, on being restored to the original plane of polarization, as if they had 

 lost nothing at all ; while the green, which has lost an odd number, will inter- 

 fere and be extinguished. The tint observed in this plane will accordingly be 

 the resultant of red and violet ; which, on account of the comparative feebleness of 

 the violet, will be but a slightly modified red. In the transverse plane, however, 

 the red and violet will interfere and be extinguished, while the green compon- 

 ents will reinforce each other, and produce their characteristic tint. 



It will be seen that the planes of polarization of the pairs of rays which pro- 

 duce the complementary effects we have been speaking of, imdergo two succes- 

 sive movements. The first movement ififrom the original plane of polarization. 

 The second movement is, for one pair of rays, similar to this, and for the other, 

 opposite. The opposite movements restore the pair of rays which they affect, 

 back to the original plane of polarization : the similar movements carry tho 

 other pair of rays into the transverse plane. 



If there Avcre no difference of path introduced in the passage of the lamina, 

 or in the case that the difference of path produced were always an even number 

 of half undulations, two movements in contrary directions would simply restore 

 the ray to its original condition, and produce no interference ; while two move- 

 ments in the same direction would extinguish it entirely. But if an odd number 

 of half undulations has in any case been lost, two successive contrary move- 

 ments will extinguish the ray, and two slmUar ones will restore its original con- 

 dition. A single half undulation of the mean ray of the spectrum lost, will pro- 

 duce a total, or almost total, extinction of the light, after two contrary move- 

 ments ; and will produce sensibly white light after two similar movements. 

 Plates so thin as to produce a difference of path less than this, Avill fail to ex- 

 tinguish the light in cither plane; but, as the thickness goes on diminishing, 

 the original plane will gain and the transverse plane will lose ; until, when the 

 thickness is zero, the light will be entirely restored in the first, and entirely 

 lost in the second. 



It is common to speak of polarized light which has passed in this manner 

 throuMi a thin crystalline lamina, as having undergone depolarization in the 

 lamina: an expression which seems to imply that it is restored to the condition 

 of common light. This, however, is not true. There is one analogy between 

 the cases, Avhich consists in the fact that the vibrations of common light, when 

 resolved into components parallel to two planes passing through the direction 

 of the ray and normal to each other, are equivalent to those of the two ray.s 

 into Avhich the one original polarized ray is divided by the lamina. But the 

 great dissimilarity of pliysical condition between the two is evidenced by the 

 fact that in the one case the analyzer produces colors, while in the other it does 

 not. There is a particular thickness of the lamina which produces something 

 more resembling depolarization. It is that at which one ray is retarded behind 

 the other a single quarter of an undulation. In this case the analyzer finds an 

 equal amount of light in both planes, and in fact in all planes ; so that, so far 

 as this test is concerned, the light is truly depolarized. But we have already 

 learned that this amount of dislocation of the rectangular components of molecular 

 movement in a plane polarized ray — the components being equal — produces 

 circular polarization. And iu fact, the most convenient mode of producing cir- 

 cularly polarized light is to employ for the purpose what is called a "quarter- 

 wave lamina." Such a lamina will convert a plane polarized ray, incident upon 

 it in azimuth 4o^ to its principal section, into a circularly polarized ray. 



When the lamina which is the subject of experiment is so thick that the 

 difference of path between the two rays amounts to many half undulations, 

 then no color can be totally extinguished in either plane. For it must be 

 remembered that each color occupies a considerable space in the spectrum, and 

 therefore has undulations belonging to it of many different lengths. The dif- 



