Invisible lenses with positive isotropic refractive index

We analyze the optical properties of the so-called invisible lenses in the wave-optics regime and show that they are practically invisible for a discrete set of frequencies. For other frequencies, the phase delay of the waves that pass through the lens compared to those that do not disturbs the outgoing waves. The frequencies for which the lens is invisible are influenced by the Gouy phase. This is the only known invisible device made of positive isotropic material at finite frequencies.