When does the choice of the refractive index of a linear, homogeneous, isotropic, active, dielectric medium matter?

Two choices are possible for the refractive index of a linear, homogeneous, isotropic, active, dielectric material. Either of the choices is adequate for obtaining frequency-domain solutions for (i) scattering by slabs, spheres, and other objects of bounded extent; (ii) guided-wave propagation in homogeneously filled, cross-sectionally uniform, straight waveguide sections with perfectly conducting walls; and (iii) image formation due to flat lenses. The correct choice does matter for the half-space problem, but that problem is not realistic.