We consider a base medium with index of refraction n containing aligned anisotropic ellipsoidal inclusions having coincident optical and geometrical axes, specified by three indices of refraction ni and depolarization factors Qi (with i = a,b,c). From Maxwell–Clausius forms for the bulk dielectric constants, we construct the difference of two indices of refraction ηa − ηb = τ (to third order in ni − n) for comparison with birefringence measurements. We obtain simple explicit expressions for τ(n) (showing both intrinsic and form birefringence) and for the special value n = nˆ corresponding to an extremum of τ. The dependence of nˆ on na and nb, and on Qa and Qb is emphasized.
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