Past exam of the physics A course of the University of Cambridge / 2015 / Paper 2 / Section A / 1

The photon relation gives $\lambda =hc/E=2.4797\times 10^{-12}\mathrm{m}$. The diffraction-limited angular scale of an aperture of diameter $D$ is thereforeFor a uniformly illuminated circular aperture, the Rayleigh criterion instead gives $1.22\lambda /D=3.03\times 10^{-11}\mathrm{rad}$. Both express the same requested estimate. This is an ideal diffraction limit, conditional on the effective diameter behaving as a coherent imaging aperture; photon energy and diameter alone do not specify the performance of a practical gamma-ray telescope.

At distance $L$, the small-angle approximation gives $\ell =L\theta$. Thus the transverse resolution is approximately $2.5\times 10^{10}\mathrm{m}$, or $3.0\times 10^{10}\mathrm{m}$ with the circular-aperture Rayleigh criterion. This is a transverse separation at the source, rather than a determination of its distance along the line of sight.