Last updated: 2026-06-16

Three Numbers That Define a Telescope

A telescope's performance comes down to a few simple ratios of its optical dimensions. From the focal length of the main optic, the focal length of the eyepiece, and the aperture, you can work out the magnification, the focal ratio, and the finest detail the instrument can show.

Magnification is how many times larger an object appears:

$M = \frac{f_0}{f_e}$

where $f_0$ is the objective focal length and $f_e$ the eyepiece focal length.

Focal ratio describes how "fast" the optics are:

$N = \frac{f_0}{D}$

with $D$ the aperture diameter. Resolving power — the smallest angle the telescope can separate — is estimated by the Dawes limit:

$\theta = \frac{116}{D\,[\text{mm}]}\ \text{arcseconds}$

Worked Example

A telescope has a 1000 mm objective focal length, a 100 mm aperture, and is used with a 10 mm eyepiece:

$M = \frac{1000}{10} = 100\times, \qquad N = \frac{1000}{100} = f/10, \qquad \theta = \frac{116}{100} = 1.16''$

So objects appear 100 times larger, the optics are f/10, and the scope can split double stars about 1.16 arcseconds apart.

Choosing Eyepieces

Because the objective focal length is fixed, magnification is set entirely by the eyepiece. A short 6 mm eyepiece on this scope would give 167×, while a long 32 mm eyepiece would give about 31×. Observers carry a few eyepieces to switch between low power for finding objects and wide vistas, and high power for detail on the Moon and planets.

Why Aperture Rules

It is tempting to chase high magnification, but aperture is what truly limits a telescope. A larger aperture gathers more light, revealing fainter objects, and resolves finer detail through the Dawes limit. Beyond about 50× per inch of aperture (2× the aperture in millimetres), extra magnification only enlarges the blur — so-called empty magnification. A 100 mm scope is useful up to roughly 200×; past that the image dims and softens rather than sharpening. The atmosphere imposes its own limit too: on all but the steadiest nights, turbulence blurs detail finer than about one arcsecond regardless of the instrument.