Remember that, for any mass, the black hole is the collapse of the mass inside it to a point or singularity of infinite density. At this point, one can use the expression above directly to obtain the required densities at for the 1 solar mass and solar mass black holes. The more careful result quoted by Bless yields densities larger than those obtained here by a factor of 100. The theoretical limit to the resolution of a telescope is set by the wave nature of light, which causes diffraction when the light passes through an aperture. To convert to arcseconds, In practice, ground-based telescopes cannot achieve this limit because of atmospheric seeing .
Real resolutions are typically of order of a few arcseconds.
Thus a single radio telescope would have to be impractically large to achieve the same resolution that a large optical telescope can theoretically obtain.