Virtual image within a transparent dielectric sphere

From the standpoint of the wave theory, we discuss the problem of an optical image formation created by a virtually converging electromagnetic wave from a light source. We solved a diffraction problem of a point source in a dielectric sphere. Formulas are obtained describing the virtual image of a point source in dielectric sphere, in the parameter range where the approximation of geometric optics is not valid. For slits in an opaque screen, the virtual image in the dielectric sphere allows the resolution of slits spaced from each other at distances much smaller than the diffraction limit $\lambda/2$. This explains the previously obtained experimental results [Z. B. Wang, W. Guo, L. Li, B. Luk'yanchuk, A. Khan, Z. Liu, Z. Chen, and M. H. Hong, Nat. Commun. 2, 218 (2011)] on the super resolution effect with virtual image.