On the theory of powell's bands and the group-velocity in dispersive media

Abstract

Powell's Bands: Observations with liquid mixtures of variable refractive index.-A description is given of the changes in the position, width and degree of visibility of the bands seen in the spectrum when a flat-sided cell containing liquid of which the refractive index is gradually varied is placed behind the prism on the table of a spectroscope, a transparent plate of glass being immersed in the cell so as to cover half the aperture. The liquid chosen for the experiment was a mixture of CS₂ and benzene of which the proportions could be altered in any desired manner. Special attention is paid to the stage at which the position of the plate in the cell has to be reversed in order that the bands might continue to be visible. Powell's Bands: Condition of visibility.-Mascart's and Schuster's statements on this point in their treatises are criticized, and it is shown that the side of the cell on which the plate should be immersed is determined not by the relation between the refractive indices of the liquid and the plate but by the group-velocities in the two media. Owing to the highly dispersive nature of the liquid employed in the experiments, the position of the plate has on this account to be changed from one side to the other at a stage at which the refractive index of the liquid is still lower than that of the plate for the whole of the visible spectrum. Powell's Bands: Relation to Laminar Diffraction.-Spectroscopic analysis of the laminar diffraction either of the Fraunhofer or the Fresnel type formed by the plate immersed in the liquid gives oblique interference lines, photographs of which are given. Their number and the positions at which they cross the spectrum are identical with those of Powell's bands and their inclination to the direction of the spectrum indicates at once the side on which the plate should be immersed for observation of Powell's bands and the degree of visibility of these bands. The visibility is maximum when the interference lines are inclined at 45° to the length of the spectrum. Group-velocity of Light: Direct determination of the position of its identity in two media.-This is rendered possible by the fact that the oblique interference lines mentioned above curve round and become inclined in the opposite direction at this position as shown in the photographs given. Determination of Refractive Indices and Dispersive Powers.-As the oblique interference-lines in the spectrum of laminar diffraction are seen clearly and sharply-defined irrespective of the thickness of the plate or the aperture of the telescope within wide limits, it is suggested that they may be used in the preference to Talbot's and Powell's bands for such determinations.