The refractive index of quartz

Abstract

The recent publication of a new series of values for the optical rotatory power of quartz, and of a new formula for its rotatory dispersion (Lowry and CoodeAdams, ‘Phil. Trans.,’ A, vol. 226, pp. 391-466 (1927)), has provided an opportunity for reconsidering the formula for the refractive dispersion of the crystal. Prior to the appearance of this paper, the characteristic frequencies which provide the dispersion-constants in Drude’s equation for optical rotatory power had always been deduced by indirect methods. Thus, the characteristic infra-red frequencies were taken (Lowry, ‘Phil, Trans.,’ A, vol. 212, pp. 261-297 (1912)) from the observations of Rubens and Nichols, who determined the wave-lengths (at 8·5 μ, 9·02 μ. and 20·75 μ.) at which the crystal behaves as a metallic reflector and gives rise to strongly marked “Reststrahlen.” The ultra-violet frequencies in Drude’s formula (which were also used in the 1912 paper cited above) were deduced, on the other hand, from the data for the refractive dispersion of the crystal; but although it was clear that two characteristic frequencies in the distant ultra-violet region must be taken into account, their magnitudes were so ill-defined that it was only possible to give a numerical value to one of them, the other being provisionally located at infinity, since a zero value was assigned to λ n 2 . In the 1927 paper, however, in order to express the numerical data with sufficient accuracy, it was found necessary to abandon finally the frequencies deduced by Drude from the other optical properties of quartz, and to work out new and independent values from the rotations themselves. Moreover, with the help of these new data it was possible not only to correct the “known” constant of Drude’s equation from λ 2 = 0·010627 to 0·01275, but also to assign a finite value to his “unknown” ultraviolet constant, the value of which was changed from λ 2 = 0 to 0·00097. The infra-red frequency, on the other hand, although its influence could not be entirely neglected, was of such small importance that its magnitude remained wholly indeterminate, even with the help of a new series of measurements of the rotatory power of the crystal in the infra-red to λ = 2·5 μ.