How does a telescope’s diameter affect its resolving power?

A telescope’s diameter, also known as its aperture, is directly responsible for its resolving power. This power defines the instrument's ability to distinguish between two closely spaced points of light, such as binary stars.

As the diameter of the objective increases, the telescope's resolving power improves, meaning it can resolve smaller angular separations. The theoretical resolving power can be calculated using the formula:

$$\text{Resolving power}=\frac{11.25\text{ seconds of arc}}{d}$$

In this formula, $d$ represents the diameter of the objective expressed in centimetres. Consequently, a larger diameter results in a smaller numerical value for the angular resolution, allowing for finer detail in observations. For example, a 25-cm objective has a theoretical resolution of 0.45 seconds of arc, while a 250-cm telescope achieves a resolution of 0.045 seconds of arc.1

This relationship exists because the finite size of the Airy disk—the diffraction pattern formed by a lens—sets an inevitable limit on resolution; larger apertures reduce the effects of diffraction spreading.2