Notes on the electromagnetic theory of light; Part I

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Abstract
On Double Refraction and the Dispersion of Oolors in pe1fectly tmnsparent .Media.1. IN calculating the velocity of a system of plane waves of homogeneous ligh t. regarded as oscillati ng electrical flu xes, in transparent and Rensibly homogeneous bodies, whether singly or doubly refracting, we may aSSllme that such a body is a very fine-grained structul'e, so tllnt it can be divided into parts having their dimensions very small in comparison with the wave-length, each of which may be regal'ded as entirely similm' to every other, INhile in the interior of each thel'e are wide diffel'ences in electrical as in other physical proverties.Hence, the average electrical displacement in such parts of the body may be expressed as a function of the time and the co()rdinates of position by the ol'dinal'y eqnat.iolls of wave-motion, while the real displacement at any point will in general cliffeI' greatly from that represented by such equations.It is th0 object of this paper to investigate the velocity of light in pCl'fect.lytranspal'ent media which have 1I0t the propertyof cil'cular polarization in a manner which shall take account of this difference between the real displacements and those repre~ented by the ordinary equations of wave-motion.We shall find that this difference will account for the dispcl'sion of colors, without affecting the validity of the laws of Huyghens and Fresnel for double refraction with respect to light of anyone color.In this investigation, it is assumed that the electrical di::;placements are solen01dal, or, in other wordR, that they are such as not to produce allY change in electrical density.The disturbance in the medium is treated as consisting entirely of such electrical displacements and fluxes, and not complicated by any distinctivel'y magnetic phenomena.It might therefore be more accurate to call the theory (as here developed) electrical rather than electromagr,el'ic, The latter term is nevertheless retained in accordance with general usage, and with that of the author of the theorv.Since the velocit'y which we are seeking is equal to the wave-length divided by the period of 08cillation, the problem reduceR to finding the ratio of these qUHntitiei', and may be simplified in some respects by supposing that we have to do with a system of stationary wave::;.rl'llnt the relation of the wave-length nnd the period is the RHIne for stationary as for progressive waves is evident from the eonsideration that a sys-
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Authors Josiah Willard Gibbs
Journal american journal of science
Year 1882
DOI
10.2475/ajs.s3-23.136.262
URL
Keywords Keywords not found

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