Fundamental limit to the use of effective medium theories in optics.

The effective medium refractive index of a surface-bound submonolayer of polystyrene nanospheres in water is found to be ill-defined below a rather specific sphere occupied area limit. The submonolayer takes on a recognizable thickness and refractive index only when the average center separation between spheres is at or below the inverse of the wavenumber. An anticipated limit to the Maxwell Garnett theory is therefore confirmed.