Telescope Magnification by Mel Bartels

Magnification is the key to using a telescope properly.

Magnification is the ratio of the apparent size to actual size of an object. For example, looking through a magnifying lens the spider appears three times bigger. That's a magnification of 3x.

A telescope is an optical instrument that makes distant objects appear closer. The optics either refract light through lenses, reflect light from curved mirrors or a combination of both.

Aperture is the area of light collected from a telescope. For example, a refracting telescope's 4 inch [10cm] diameter lens or a reflecting telescope's 12 inch [30cm] primary mirror diameter.

Focal length is the length of the focus of the telescope; the eyepiece focal length is the focal length of the eyepiece.

A telescope forms a real image, which can be seen in daytime or when aimed at the Moon. The eyepiece projects the real image to form a virtual image for the eye.

Magnification depends on telescope focal length and eyepiece focal length. Calculate magnification by dividing the telescope focal length by the eyepiece focal length. For example, a 6 inch or 15cm telescope of 48 inches focal length used with a 9mm eyepiece yields a magnification of 48 inches * 25.4mm per inch / 9mm = 135x.

Astronomical objects are very far away and very faint. Both magnification and aperture are needed to view and image objects.

Astronomical objects are either point sources like stars, too small in diameter to ever be resolved in a telescope, or extended sources like nebulae.

There is a practical limit to both lowest magnification and highest magnification.

The lowest magnification is simply the ratio of the telescope's aperture to the eye's dark adapted pupil. The lowest possible magnification for a 6 inch or 15cm aperture is 6 inches * 25.4mm/inch / 7mm eye-pupil = 22x.

A useful highest magnification is the magnification where the eye's resolving power is fully utilized. A telescope's resolution is limited by interference caused by the aperture. The interference creates a disk of light surrounded by ever fainter rings of light. The radius of this Airy Disk is ~ 1.2 times the wavelength of light divided by the aperture. For a 6 inch or 15cm aperture scope the Airy Disk is 0.75 arc-seconds. The eye can resolve 120 arc-seconds. The magnification that matches the eye's resolution to the telescope's resolution is 120 arc-seconds divided by 6 inches aperture or roughly 27x per inch of aperture (roughly 68x per cm of aperture).

Many observers prefer up to twice this amount so that the eye isn't strained (54x per inch of aperture or 136x per cm of aperture).

Magnification above this is termed empty magnification: the object is made larger but nothing more can be resolved. In certain cases such as double star observing increasing magnification above this amount makes measuring the separation between the stars easier, but otherwise the image becomes softer, fuzzier and displeasing to the eye.

Shimmering in the atmosphere, called seeing also limits magnification. If the jet stream is overhead or the upper atmosphere otherwise disturbed, magnification can be limited to 250x regardless of aperture. Steadier nights allow for increased magnification. The number of nights where 500x or higher can be employed are few in number and highly prized by observers. Nights where 2000x and higher can be used come once a decade. For example see The Night of 6000x at the 1997 Oregon Star Party. For more on seeing and the atmosphere, see my article on atmospheric turbulence.

A useful range of magnification for many telescopes is 50x to 250x. Richest Field Telescopes and binoculars employ lowest power for the widest fields.

Stars (other than our Sun) are so far away that they are not resolvable regardless of magnification. They remain point sources. Extended objects (Moon, Sun, planets, nebulae, galaxies), however, are resolvable. As magnification increases, their light is spread over a larger area, decreasing brightness at any single point. The Moon, Sun and planets are so bright that increasing magnification doesn't consign them to invisibility. Nebulae and galaxies are a different matter.

Let's use the Andromeda Galaxy, visible as an elongated smear in dark skies to the unaided-eye. It's about 3x1 degrees apparent size with an integrated or overall magnitude of 3.5. The galaxy has an average surface brightness of 22.2 magnitudes per arc-second square. Let's use our 6 inch, 15cm, aperture at lowest magnification of 22x. At 22x the Andromeda Galaxy now appears 66x22 degrees in size and will comfortably fit within a 80 degree field of view eyepiece. The telescope brightens the galaxy by the ratio of the square of the telescope's aperture to the eye's aperture, or (6 inches of aperture * 25.4 mm/inch / 7mm eye-pupil) squared or 484 times. But the magnification of 22x decreases the object's brightness by the identical 484 times amount, leaving the apparent average surface brightness unchanged at 22.2 magnitudes per arc-second. Yet the view through the 6 inch is immeasurably richer. Why?

Balancing aperture with magnification is as if a rocket ship takes us 22 times closer. We see more detail and the object overall is much brighter. But fly too close and the eyepiece can no longer fit the object into the field of view. Using the same telescope at increasing magnification means more detail at the cost of brightness. See my comparison of the Sombrero Galaxy, M104, with 6 inch and 13 inch telescopes at is aperture king?

For optimal off-axis masks at given magnifications, see off-axis masks.

Table of lowest and highest magnifications per aperture.

Lowest magnification is given for 7mm and 5mm pupils, older people's eyes being closer to 5mm. Magnifications starred with an asterisk * may be limited by seeing conditions.

Aperture Lowest Mag Lowest Mag Highest Mag Highest Mag
inches 7mm pupil 5mm pupil
doubled
0.3 1 1 7 15
1 4 5 27 54
2 7 10 54 108
4 14 20 108 216
6 22 30 162 324*
8 29 40 216 432*
10 36 50 270* 540*
13 45 63 338* 675*
14 51 71 385* 770*
16 58 80 432* 864*
18 65 90 486* 972*
20 72 100 540* 1080*
22 79 110 594* 1188*
24 86 120 648* 1296*
25 90 125 675* 1350*
28 101 140 756* 1512*
30 108 150 810* 1620*
36 130 180 972* 1944*
40 144 200 1080* 2160*
48 173 240 1296* 2592*
60 216 300* 1620* 3240*

Choosing magnification and aperture.

Start with an object in mind. Three examples...

Saturn. Since Saturn is a planet, select for highest useful magnification for your telescope, given seeing conditions. For example at my home, some of time I can I am limited to 250x, sometimes I can get up to 500x, occasionally I can reach 1000x before the image turns fuzzy thanks to seeing.

North American Nebula. The NAN is an extended wide field object, spanning 120 arc-minutes.

Compute the highest magnification such that the entire object plus a border fits into the eyepiece. For this we need to know your eyepieces apparent field of view.

Eyepiece apparent field of view is object size in arc-minutes is

Highest magnification is and largest aperture is

Dumbbell Nebula. This planetary nebula is a favorite of observers. Its size is about 8 arc-minutes. Enter its size in the calculator above. The calculator will give a value of 240x-600x depending on the eyepiece's apparent field of view. The calculator will also give an aperture value far greater than your telescope. In this situation, use the largest aperture you have, setting its magnification to the calculated amount.

If the object is too faint, then use a slightly lower magnification. If the object is too fuzzy because of turbulence in the atmosphere or perhaps because the telescope is performing poorly, then lower the magnification. Be careful to not over-magnify the object such that it overfills the field of view. This can cause a faint object to disappear.

Here is a table of magnification and aperture for objects of different size. The aperture is based on a 7mm eye pupil. For 5mm eye pupil, increase magnification by 1.4 and decrease aperture by 1.4. Magnifications starred with an asterisk * may be limited by seeing conditions.


Eyepiece apparent field of view

60 degrees 80 degrees 100 degrees
Object size
arc-minutes
magni-
fication
aperture
inches
magni-
fication
aperture
inches
magni-
fication
aperture
inches
180 16x 5 22x 7 27x 8
120 24x 7 32x 9 40x 12
60 48x 14 64x 18 80x 23
45 64x 18 85x 24 107x 30
30 96x 27 128x 36 160x 45
15 192x 54 255x* 71 319x* 89
8 359x* 100 478x* 133 597x* 166
4 717x* 200 956x* 266 1194x* 332
2 1433x* 399 1911x* 531 2388x* 664
1 2866x* 796 3821x* 1062 4776x* 1327

The strategy is to select the highest magnification that frames the object in the eyepiece's field of view, subject to seeing conditions and telescope capabilities. Then select the largest aperture available. Starting with a given aperture, select for the highest magnification that frames the object, subject to seeing. If the object is invisible, then try a lower magnification. This rarely happens. Much more common is a failure to properly frame the object. Use filters, go to dark skies and improve your observational skills.

Should you ever select for less aperture? That's equivalent to stopping down the aperture to improve the view. Stopping down by using an off-axis mask to reduce the deleterious effects of bad seeing helps. Stopping down to improve deep-sky views does not help. While objects can be detected at diminished apertures, there is a general loss of detail. See my results at Is aperture king?

As long as you can select for the largest aperture, you are in telescope mode. Once aperture is constrained, you are in eyepiece mode. Well equipped amateurs who have a number of eyepieces should also consider equipping themselves with a range of apertures.

Note that wider angle eyepieces allow for greater aperture.

For more information see
Why am I seeing more?
A new way to look at things
Bartels' equation for telescope value
Tips to improve your telescope

For my telescopes and more articles, see my Telescope Making page.

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