Magnification and eyepieces

8 min read

Key facts

Magnification formula	Telescope focal length ÷ eyepiece focal length
Example	1,200 mm ÷ 25 mm = 48x
Focal ratio	Focal length ÷ aperture (1,200 ÷ 150 = f/8)
Maximum useful magnification	About 50x per inch of aperture
True field of view	Apparent field ÷ magnification
Exit pupil	Aperture ÷ magnification
2x Barlow lens	Doubles the magnification of any eyepiece
Usual limit on ordinary nights	About 150x to 250x, set by the atmosphere

In short

Magnification is not fixed: divide the telescope's focal length by the eyepiece's focal length.
Shorter eyepieces give higher magnification, but a dimmer, smaller field of view.
Useful magnification tops out around 50x per inch of aperture, and turbulent air often limits it further.
Low power is best for finding objects and for large clusters; high power for the Moon, planets and double stars.
A Barlow lens multiplies the power of every eyepiece, effectively doubling a small collection.

Magnification is set by the eyepiece

A telescope has no single magnification. Every telescope has a focal length, the distance from its main lens or mirror to the point where it brings light to focus, and every eyepiece has its own, much shorter, focal length. Magnification is simply the first divided by the second.

Both numbers are usually printed in millimeters: on the telescope tube or its label, and on the side of each eyepiece. Swap eyepieces and the magnification changes. That is why one telescope can show the whole Pleiades cluster one moment and a close-up of a single lunar crater the next.

Worked examples

Take a telescope with a focal length of 1,200 mm. With a 25 mm eyepiece, 1,200 ÷ 25 gives 48x. With a 10 mm eyepiece, 1,200 ÷ 10 gives 120x. With a 6 mm eyepiece, the result is 200x.

Now a shorter telescope with a 650 mm focal length. The same 25 mm eyepiece gives 26x, and the 10 mm gives 65x. The same eyepiece produces different magnifications on different telescopes, so always do the calculation for your own setup.

Focal ratio: fast and slow telescopes

The focal ratio, written as f/ followed by a number, is the focal length divided by the aperture. A 1,200 mm telescope with a 150 mm (about 6-inch) mirror is f/8; a 650 mm telescope with a 130 mm mirror is f/5.

Low numbers are called fast and give wider views at a given eyepiece, which suits large star fields. High numbers are called slow and reach higher magnification more easily, which suits planets. The focal ratio does not change how bright an object looks to the eye at a given magnification; aperture does that.

The maximum useful magnification

Magnification spreads the light over a larger image, so beyond a certain point the view only gets bigger, dimmer and blurrier. A widely used guide is about 50x per inch of aperture, or roughly 2x per millimeter. A 4-inch telescope tops out near 200x; an 8-inch near 400x.

Those figures are best-case limits. In practice most observing happens far below them, and the lowest power that shows what you want is usually the most pleasing. Claims of 500x or more on a small telescope describe empty magnification: bigger, but showing nothing new.

Field of view and exit pupil

Each eyepiece has an apparent field of view, the angle you see when looking into it, often 50° to 70° or more. Divide that by the magnification to get the true field, the actual slice of sky. A 50° eyepiece at 48x shows about 1°, roughly two Moon widths; at 200x it shows only a quarter of a degree.

The exit pupil is the width of the beam of light leaving the eyepiece: aperture divided by magnification. A 150 mm telescope at 48x gives about 3 mm. Large exit pupils, 4 to 7 mm, give bright, wide views of faint nebulae; small ones, 0.5 to 1 mm, are near the useful limit for planets and double stars.

Barlow lenses and choosing a set

A Barlow lens is a short tube that goes between the telescope and the eyepiece and multiplies the effective focal length, usually by 2x or 3x. A 2x Barlow turns a 25 mm eyepiece into the equivalent of a 12.5 mm one, so two eyepieces plus a Barlow give four magnifications.

A practical starting set covers three steps: a low power for finding objects and viewing large clusters, a medium power around 80x to 120x for general use, and a high power for the Moon and planets on steady nights. Choose eyepiece focal lengths so the Barlow fills gaps rather than duplicating them.

Seeing: the atmosphere sets the limit

Astronomers call the steadiness of the air seeing. Pockets of warmer and cooler air make starlight shimmer, which is why stars twinkle. On many nights that turbulence blurs detail beyond about 150x to 250x, no matter how large the telescope.

To make the most of a night, let the telescope cool outdoors, observe objects high in the sky rather than near the horizon, and avoid looking over rooftops or warm pavement. Start low, increase magnification until the image softens, then step back one eyepiece. And never aim a telescope at the Sun unless a certified ISO 12312-2 solar filter fully covers the front.