We discuss the calculation of the refractive index by means of the ab initio
scalar dielectric function and point out its inherent limitations. To overcome
these, we start from the recently proposed fundamental, microscopic wave
equation in materials in terms of the frequency- and wavevector-dependent
dielectric tensor, and investigate under which conditions the standard
treatment can be justified. Thereby, we address the question of neglecting the
wavelength dependence of microscopic response functions. Furthermore, we
analyze in how far the fundamental, microscopic wave equation is equivalent to
the standard wave equation used in theoretical optics. In particular, we
clarify the relation of the "effective" dielectric tensor used there to the
microscopic dielectric tensor defined in ab initio physics.Comment: consistent with published version in Eur. Phys. J. B (2020
