Beginners sometimes wonder what eyepieces to get for a new telescope, and what eyepieces are all about in general. Eyepiece design and performance is fascinating, and many technical sources explain what's what, but I would like to give some simple, practical comments that might otherwise get lost in minutia.

Introduction:

Basic terminology, arithmetic, and how-does-it-work stuff:

Thus a telescope with a 1000 mm focal length, used with an eyepiece of 25 mm focal length, has a magnification of 1000 / 25, or 40. It makes things look 40 times wider, or if you prefer, 40 times closer. Put in an eyepiece with 4 mm focal length, and the same telescope now has magnification of 1000 / 4, or 250.

Magnification is sometimes symbolized by the letter "X" (or "x"). Thus we might speak of 40x, or 250x, and a 7x50 binocular magnifies seven times. (The "50" is the diameter of its front lenses, in millimeters.)

Focal lengths of commercially available telescope eyepieces range from 2.5 mm to 60 mm or more.

Thus if you are using an eyepiece with an apparent field of view of 50 degrees, in combination with a telescope such that its magnification is 100x, the width of the actual field of view will be about 50 degrees / 100, or 0.5 degree -- about the width of the full Moon.

4) Eyepieces come with different barrel diameters -- the diameter of the cylindrical part of the eyepiece, that fits into the telescope's eyepiece holder. There are three common sizes on the market today, and one less common one. The common barrel diameters are 2.00 inches, 1.25 inches, and 24.5 millimeters (0.965 inch). The less common one is 23 mm (0.917 inch).

Barrel diameter has nothing to do with magnification. But too small a barrel may restrict the apparent field of view of a long focal-length eyepiece.

Barlow lenses on the commercial market come in at least the three common barrel diameters, and have focal-length multiplication ratios from 1.75 to 5.00. Some have adjustable multiplication ratios.

Sufficient eye relief is a good thing. Too little is vexing. Too much can be vexing, too -- sometimes you can have trouble figuring out where to put your eye.

In general, for eyepieces of the same design, eye relief increases in proportion to focal length. But at constant focal length, it varies enormously from design to design. Several lines of eyepieces have been designed specifically to provide the same, ample, eye relief over a wide range of focal lengths.

Generalities about Eyepiece Selection:

2) A small number of good eyepieces is better than a large number of bad eyepieces.

3) Not all Barlow lenses work well with all telescopes and eyepieces. You have to try the combinations you have in mind, and find out what works.

4) It is ultimately desirable, to have eyepieces that provide a nicely-spaced sequence of magnifications along a useful range for your telescope. Yet some magnifications are more useful than others. It makes sense to buy those first. I have an opinion on what they are:

I recommend starting with two eyepieces, one with magnification of about one-fifth the aperture of your telescope, expressed in millimeters, and the other with magnification about equal to the aperture in millimeters. That is, for a six-inch telescope -- 152 mm -- I recommend you start with magnifications of about 30 and about 150. I won't complain if they are 25 and 120, or 40 and 200.

The more powerful eyepiece gives a magnification most of us would call "medium". It will be the one you use in decent seeing, to look at the Moon, planets, and double stars. The other one will give brighter images of faint nebulae and galaxies, and so make them easier to see than if their limited light were spread wide, by high magnification.

The low-magnification eyepiece will also do double duty for finding things. Thus it should have a field of view as wide as possible, and that means that its front lens should be as big in diameter as possible, subject to two limits -- your budget (wide-field eyepieces are expensive), and the diameter of the focus tube of your telescope (wide lenses won't help if telescope parts get in the way). If you have a telescope with a long focal ratio (big "f" number), with a small-diameter focus tube, then you won't be able to get a wide-field view, but you will still want a low magnification for faint fuzzies.

If you have money left after buying these two eyepieces, and if you absolutely cannot wait until you have joined a club and tried things out, then the next two magnifications you will want will probably be one a little less than the half-way point between the first two -- say, 65x to 75x on a six-inch -- and one at not quite twice the magnification of the more powerful of the first two -- say, 250x on a six-inch.

Specific Recommendations:

Here are recommendations for the "first two", for common telecopes.

f/10 Schmidt-Cassegrain, Maksutov, or refractor -- Get a 10 mm Orthoscopic or Plossl. Then, if you have a 1.25-inch focuser, a 40 mm Plossl or Kellner in that diameter will do nicely -- several vendors carry them -- or maybe a 32 mm if you find the narrow field of the 40 mm aesthetically unappealing. With a two-inch focuser, Meade, Pentax and University Optics have suitable 40 mm eyepieces. None are cheap.

Many of these telescopes come with a decent 25 mm or 26 mm eyepiece as standard equipment. If so, keep it for a while, and just buy the 10 mm.

Small "beginner" refractor, f/10 to f/12, with 0.965-inch focuser -- The right answer for 0.965-inch focusers is a "hybrid" star diagonal that fits the focuser and accepts 1.25-inch eyepieces. The focuser restricts the field of view, but there are lots more eyepieces to choose from at 1.25-inch diameter than at 0.965. You can then go for a 10 or 12 mm Orthoscopic or Plossl, and a 40 mm Plossl or Kellner. But BE CAREFUL, not all small refractors will come to focus with a hybrid diagonal in place, and a 40 mm Plossl may be too big and clumsy for such a small telescope. If the hybrid diagonal does not work for you, you will have to hunt down eyepieces with 0.965-inch barrels in appropriate focal lengths. 10 or 12 mm should be no problem, but you will be lucky to find a decent eyepiece of that barrel diameter with a focal length over 30 mm.

An Approach to Technical Minutia:

Switching eyepieces enables a tradeoff among three important, related quantities; namely

Image brightness of extended objects (like nebulae), and

Width of field of view.

Magnification:

Some folks think high magnification is what telescopes are all about, but there is a lot more to it. If an object is sufficiently bright to begin with, then increasing magnification up to certain a point will generally allow you to see more details. But, where is that "certain point"? There is no single answer. If you increase the magnification of your telescope in small increments, there are several reasons why you might want to stop after a while. They include:

b) Jiggly mounting. Not only must the atmosphere be steady, but so also must be the mounting of your telescope, if the images are not to look wiggly.

c) Less than perfect telescope optics. Other things being equal, poor optics will give a blurrier image than good optics. There's no point magnifying detail that isn't there!

Even a telescope with good optics may temporarily misbehave when it is first set up, before all the parts have cooled to the temperature of the surrounding air. Large amateur telescopes may take hours to settle to temperature. The problem is worse in winter than in summer.

This matter is rarely understood, so I repeat: There is a limit to the amount of detail in the image of even a perfect telescope, and there is no point in using more magnification than it takes to see all of it.

Image Brightness:

This discussion is closely related to the material in paragraph (e), immediately above. The image brightness of an unresolved point of light -- like a star -- does not change as you change magnification, at least, not until the magnification is high enough so that you can begin to see the diffraction pattern of the star. The brightness of an extended object, however, declines as the square of magnification -- twice as much magnification reduces the image brightness by a factor of four. Reducing brightness will eventually make objects and their details harder to see, but on the other hand, increasing magnification does make those details larger. It is not always obvious which way the tradeoff works -- does increasing magnification gain more by enlarging details than it loses by making them fainter? You have to try it and see.

You might think that the best way to see faint extended objects is therefore to use a very low magnification, which makes their images as bright as possible. That doesn't always work, either. The eye behaves in a more complicated manner: Sometimes the tradeoff between image size and brightness favors a larger, dimmer image: I often have best luck looking at distant, faint galaxies at a magnification of about two-thirds the telescope clear aperture in millimeters (100x on a 150 mm telescope), which is a lot more magnification than many books say to use for deep-sky observation. Sometimes, also, it seems to help to have a magnification great enough that the background sky looks black -- at very low magnifications, it may look gray, and that seems to make faint things harder to see.

At very low magnifications, another thing begins to happen. The diameter of the beam of light coming out of an eyepiece -- which is called the "exit pupil" -- is equal to the telescope clear aperture divided by the magnification (thus a 150 mm telescope used at 100x has a 1.5 mm exit pupil). It turns out that the exit pupil can also be calculated as the eyepiece focal length divided by the focal ratio of the telescope (thus any f/10 telescope used with a 15 mm eyepiece will have a 1.5 mm exit pupil). When the exit pupil is bigger than the pupil of the observer's eye, not all the light that comes out of the telescope can make it to the observer's retina -- some will be blocked by the pupil of the eye. Once magnification has dropped so far that that has started to happen, then further reductions in magnification do not make the images of extended objects any brighter. Extended object surface brightnesses stay the same, and images of point sources (like stars) get dimmer, as magnification decreases further.

The diameter of the pupil of the dark-adapted human eye varies from person to person, but tends to decline with age. As a rule of thumb, persons younger than about 40 will likely have dark-adapted pupils of 7 mm diameter; older people will have smaller ones. But I do not generally recommend magnifications that produce exit pupils larger than four or five millimeters anyway.

There is a special case: If you have a fast (small f-number) telescope, and need a very wide field eyepiece to find things, or for spectacular views of very large objects, then perhaps you have cause to get a very low-magnification eyepiece, even if it has an over-large exit pupil. You will be throwing away light, but perhaps the wider field is worth it to you.

Field of View:

For eyepieces of a given design (Kellner, Orthoscopic, Plossl...) the width of the field of view is generally inversely proportional to the magnification -- doubling the magnification cuts the field width in half. But at the same magnification, different eyepiece types have dramatically different fields of view -- expensive modern designs, like Naglers, may have twice as wide a field as such old standbys as Kellners and Orthoscopics. So if you want a wide field of view, perhaps for finding things or for looking at some of your favorite large objects, you must either get a long focal-length, low-magnification eyepiece, or spend some money for a fancy design, or both.

There is a catch, too: There is no magic to getting a wide field of view in an eyepiece -- look down the barrel of a short focal-length, high-magnification eyepiece, and see how tiny the lenses are compared to those in a low-magnification eyepiece. Wide fields of view require wide lenses. But wide lenses won't do any good if the eyepiece barrel, or the focuser tube, or the baffle tube of a Schmidt-Cassegrain, prevents light from getting to their outer edges. For good use of a low-magnification, wide-field eyepiece design, it must be mounted in a large eyepiece barrel and used with a large-diameter focuser and baffle tube. A 40 mm eyepiece will give a nice low magnification in an f/10 refractor or in a Schmidt-Cassegrain, but it must be have a two-inch barrel and be used in a two-inch focuser, if it is to give a wide field of view, as well.