Optical rotatory dispersion of crystals

Abstract

Many formulae have been proposed to express the rapid increase of the rotatory power of quartz with diminishing wavelength. These consist mainly of terms of the Drude type, namely ρ = ∑ r Q r λ 2 − λ r 2 , , and require a large number of constants to fit the measurements in the ultra-violet region of the spectrum. It is shown in this paper that the entire range of data from the visible to the remote ultra-violet is accurately represented by the following simple formula ρ = k λ 2 ( λ 2 − λ 0 2 ) 2 , , where ĸ = 7.19, and λ 0 =0.0926283 μ . A theoretical interpretation of the formula is given on the basis of a coupled oscillator model. It is suggested that the rotatory power of quartz arises primarily as a result of an interaction in the nature of a resonance between the similar polarizable units constituting the crystal. This type of interaction causes a splitting of the characteristic frequencies of each individual unit, and the expression for the rotatory power is consequently of the quadratic form. Formulae are also given for sodium chlorate, cinnabar and benzil, all of which, like quartz, are optically active only in the crystalline state. The applicability of the quadratic formula to these cases is discussed.