Average value of the shape and direction factor in the equation of refractive index

摘要

The theoretical calculation of the refractive indices is of great significance for the developments of new optical materials. The calculation method of refractive index, which was deduced from the electron-cloud-conductor model, contains the shape and direction factor < g >.< g > affects the electromagnetic-induction energy absorbed by the electron clouds, thereby influencing the refractive indices. It is not yet known how to calculate < g > value of non-spherical electron clouds. In this paper, < g > value is derived by imaginatively dividing the electron cloud into numerous little volume elements and then regrouping them. This paper proves that < g > = 2/3 when molecules' spatial orientations distribute randomly. The calculations of the refractive indices of several substances validate this equation. This result will help to promote the application of the calculation method of refractive index.