White-Light Interference Fringes with a Thick Glass Plate in One Path

Abstract

In Part I of this paper [1] the writer developed a theory of the white-light fringes observed in the Michelson interferometer when a thick plate of glass, or other refractive substance, is placed in one of the paths. Part I treated of the axial beam, whose composition determines the color of the central spot in the fringe pattern. An explanation was given of the very great number of colored fringes, running up to several thousand, which is observed under these conditions. In this part we discuss certain phenomena which depend for their explanation upon the analysis of a beam oblique to the optical axis. To observe these phenomena we obtain, as described in Part I, circular fringes in sodium light, insert the thick plate in one of the paths, shorten that path until in the neighborhood of the most brilliant sodium maximum, in which position colored fringes will be seen with white light. If we observe these fringes through a spectroscope with the slit placed across the center of the system, the slit being long enough to cut across the whole field, the spectrum is seen to be crossed by a system of concentric dark rings, looking very much like a shadow of the fringe system itself. If now one of the paths is slowly shortened or lengthened, these dark rings expand or contract, as the case may be, just as in the fringe system. In addition, the center of the system on the spectrum travels very slowly from one end of the spectrum to the other. These phenomena may be observed easily and distinctly if a rather wide slit, cut in a card, is placed in the path of the light before it enters the interferometer, and the fringes are then viewed through a direct-vision spectroscope, without slit.