Dispersion Relations for the Refractive Indices and the Effective Birefringence of Liquid Crystals

Dispersion relations for the optical dielectric constants ϵ⊥ and ϵ∥ of liquid crystals are derived using Vuks' relation. These relations have three advantages over existing dispersion relations of the molecular birefringence Δ: 1) there is no need for having the resonance wavelength of the nearest absorption band, 2) no approximations are involved in their derivation. and 3) they are useful for calculating the effective birefringence of liquid crystals which depends on ϵ⊥ and ϵ∥ separately rather than on δ Excellent agreement is found with the available experimental results.