. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. CHROMATICS OF POLARIZED LIGHT FORMULAE. 207 ^'P-^^. feronces may be slight, but slight values many times repeated become largo values at last; so that two red rays whose phases are for several undulations sufficiently unlike to conflict, may, after a larger number, be nearly enough alike to conspire. If the numbers 21 and 22 represent the lengths of two undulations of green, after a retardation of eleven times the length of the former, the
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. CHROMATICS OF POLARIZED LIGHT FORMULAE. 207 ^'P-^^. feronces may be slight, but slight values many times repeated become largo values at last; so that two red rays whose phases are for several undulations sufficiently unlike to conflict, may, after a larger number, be nearly enough alike to conspire. If the numbers 21 and 22 represent the lengths of two undulations of green, after a retardation of eleven times the length of the former, the latter will have fallen half an undulation behind it. Thus, after a certain amount of retardation is reached, there will be found rmdulations of all colors im- part irdl}' distributed through all varieties of phase, and the chromatic phenomena above described will cease. A general expression for all these phenomena may be found as follows : Let PP' be the plane of jjolarization of the original ray; QQ' the princi- pal plane of the lamina; 1111'the conjugate plane; 1)0' the principal plane of the analyzer, which we will suppose to be a doubly refracting prism or rhomb of Iceland spar; and EE' its conjugate plane. Draw PA, PB, perpendicular to QQ'and IIR'; BE, BG perpendicular to EE',00'; and AD, All perpendicular to EE', 00'. Then if CP rep- resent the velocity of molecular movement in the original ray, C A and CB will represent its equiva- lent components in the directions IMl and Q'Q. If these components be further decomposed in the directions 00' and EE', we shall have the original velocity CP represented by the four elements CCr, GII in the principal plane, and CD, CE in the con- jugate plane of the analyzer. Ilepresent the original velocity CP by V. Put the angle PCQ=«, and the angle PC()—j. Then the angle OCQ w'iU be a—,3. The triangles PC A, PGB giveCA=Vsina; CB=Vcosa. And the triangles ACD = ACH, and BCE=BCG, give CD=Vsinacos(«—p') ; CF = Vcorjasin(a—,3); CG=Vc
Size: 1495px × 1671px
Photo credit: © Library Book Collection / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorsmithsonianinstitutio, bookcentury1800, bookdecade1840
