Why does a larger telescope aperture improve resolving power?
A larger telescope aperture improves resolving power because it reduces the size of the Airy disk, which is the diffraction pattern formed by a point source of light.1
When light passes through a lens or mirror, it undergoes diffraction, creating a central dot surrounded by rings of light. The finite size of this pattern sets an inevitable limit on the instrument's ability to distinguish between two closely spaced objects. According to the Rayleigh criterion, two adjacent light sources can be resolved only if the image of one falls near the innermost dark ring of the other's Airy disk.1
Because the angular resolution is inversely proportional to the diameter of the objective, a larger aperture produces a smaller Airy disk. This allows the telescope to distinguish between points with a smaller angular separation, effectively increasing the instrument's ability to resolve fine detail in celestial objects like binary stars.12