Focal shifts on focusing through a plane interface

We derive explicit formulas for the focal shift, the intensity increase, and the axial zeros obtained on focusing at low Fresnel numbers through a plane interface between two isotropic media, and demonstrate their validity through comparisons with numerical plots of axial intensity distributions. Also, we show that for the special case in which the two isotropic media have the same refractive index, these formulas are in complete agreement with previous results presented for focusing in a single medium.