CRYSTALLINE PLATES IN POLARIZED LIGHT. 



205 



In the fourth place, the principal plane of the lamina shonld, in order to produce 

 the most complete interference, be at an azimuth of 4''3'- to the plane of original 

 polarization — the two rays being, in this position of the crystal, exactly e(jual 

 to each other. In the fifth place, we must observe the phenomena by means of 

 an analyzer, which allows only the light polarized in a single plane to come 

 to the eye, or which, like a doubly refracting prism, separates the emergent 

 light which is polarized in one plane from that Avhicli is i)olarized in tlu; trairs- 

 verse plane ; otherwise in this case again we shall have; the blended efiects of 

 two compensatory interferences. Finally, the principal plane of the analyzer 

 should, in order to produce the best effect, be at an azimuth of 45° from the 

 principal plane of the lamina. The necessity of this coiidition may be readily 

 deduced from the law of Mains. The annexed figure may illustrate the changes 



which take place in the passage of the ray 

 ^Bco through the system. If the arrow, P, rep- 



_2?/ ^-^^^^^^M^ resent the direction of an elementary mo- 



^^^f'"" lecular movement of the original polarized 

 ray, this movement will be resolved in the 

 lamina into two movements at right anglea 

 ''^' "■'' to each other, and each inclined 45° to V, 



as shown by the arrows Ro {^^(^ ordinary ray) and Ilg (the extraordinary.) 

 Suppose these rays to emerge, without difference of path, from the lamina, and 

 to be received upon a crystal of Iceland sj)ar whose principal plane coincides 

 with the direction of P. .Then R^ will be resolved into Rqo and Roe; and R^ 

 will be resolved into Roo and Rye- Rqo and R^o will conspire, and Roo and R^.^ 

 will conflict. The first pair, on the supposition we have made, v.'ill only bo 

 effective. The second will destroy each other. 



But Ro is retarded (in the case of a negative crystal) behind R^,. Let the 

 retardation amount to an odd number of half undulations, and the arrangement 



of the illustrative arrows will be what is 

 seen here. In this case the pair in the prin- 

 cipal plane of the analyzer conflict and arc 

 destroyed ; while the pair in the transverse 

 plane conspire. And this represents Avhat 

 actually occurs, when the thickness of the 

 lamina is such as to produce exactly the 

 amount of retardation here supposed. 

 But since the undulations of the component rays of white light are unequal 

 in length, the retardation which will be sufficient to suppress one color, will not 

 entirely suppress the others. The ray R„o+Reo will not therefore be wholly 

 extinguished, but will exhibit a color which will be the resultant of the unsup- 

 pressed tints. Moreover, the retardation which produces perfect coincidence in 

 the ray Roe-f Ree for o^^ color, will not do the same for the rest. There will 

 therefore be a color in this ray also, in which the tint suppressed in the other 

 plane will be predominant. It is to be observed, however, that when the plate is 

 so extremely thin that the retardation suffices only to produce a difference of 

 path equal to a single half undulation of the mean ray of the spectrum, or less 

 than this, no color will appear. And the reason will be obvious, if Ave consider 

 that, though the undulations of the different colors are unequal, their inequal- 

 ities as compared with the total length of the mean undulation are not great. 

 The undulations of the middle violet, middle green, and middle red — the extreme 

 and mean colors of the spectrum — are approximately in the ratio of the-num- 

 bers 17, 21, and 26. A retardation of half an undulation of the green would 

 therefore be about the fourth part more than a half undulation of the violet ; 

 and a fifth part less than a half undulation of the red. But a retardation of 

 Jive half undulations of the green Avouhl be not far from six half undulations 

 of the violet or Jour of the red. The violet and the red, therefore, having in 



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