Resolving Power of an Astronomical Telescope

For an astronomical telescope, the same Rayleigh criterion is applied to the diffraction pattern formed at the circular aperture of the objective (lens or mirror), of diameter $D_{ap}$, rather than to a slit -- the mathematics of diffraction at a circular aperture differs in detail from the single-slit case worked out earlier, but leads to a directly analogous first-minimum condition. The smallest angular separation $d\theta$ between two distant point objects (two stars, say) that the telescope can still show as two separate images -- its limit of resolution -- works out to

and the resolving power of the telescope, the reciprocal of this angle, is

$\text{Resolving power}=\frac{1}{d\theta}=\frac{D_{ap}}{1.22\,\lambda}$ …