Q.What is meant by the resolving power of an astronomical telescope? State the factor on which it depends, and explain why astronomical telescopes are built with objectives of as large a diameter as possible.

The resolving power of an astronomical telescope is its ability to form separate, distinguishable images of two point objects (such as two close stars) that are only very slightly separated in angle as seen from Earth; it is defined as the reciprocal of the smallest angular separation $d\theta$ the telescope can still resolve, by the Rayleigh criterion applied at the circular aperture of the objective.

This limit of resolution works out to $d\theta=1.22\lambda/D_{ap}$, so the resolving power $1/d\theta=D_{ap}/(1.22\lambda)$ depends directly on the diameter $D_{ap}$ of the objective (lens or mirror) and inversely on the wavelength of light used. …

Recall that resolving power is the reciprocal of the diffraction-limited angular resolution $1.22\lambda/D_{ap}$, and …

• Confusing resolving power with light-gathering power -- a larger aperture does both, but the reasoning asked for here is specifically about the diffraction-limited ANGULAR resolution. …