No telescope is complete without eyepieces, and no astronomical accessory is so seemingly complicated, either. There are a million different ones, with a welter of different specs, available from a horde of manufacturers and distributors. No wonder the person starting out into astronomy gets a headache when they try to figure out what they need.
The purpose of any telescope is to show us celestial objects and the size that these objects appear is set by the magnification. In turn, the magni- fication is set by the focal length of your telescope and the focal length of the eyepiece in use with it. That is:
Magnification = F/f where: F is the telescope focal length f is the eyepiece focal lengthAny given telescope will only support a certain range of magnifications, limited in one way or another by four things:
a. Telescope focal length b. Eyepiece diameter c. The unsteadiness of the atmosphere, or 'seeing' d. Telescope apertureThe lower end of the magnification range is controlled by the eyepiece diameter. Light coming out of the telescope must fit into the eyepiece, and smaller diameter eyepieces just can't fit in as much of it as their larger diameter cousins. This is similar to looking through a pipe; you can see a wider area through one a bigger one. For high magnifications this diameter limit isn't a problem because you're only looking at a small area of the sky, but it becomes important when you want wider fields of view.
There are three diameters of eyepieces usually sold. The smallest are 0.965" in diameter; they are the least common and is generally associated with small, less-expensive scopes (there are exceptions). Most popular are the 1.25" diameter eyepieces, and for most scopes these are perfectly adequate. Also commonly found are the 2" diameter eyepieces, especially among owners of longer focal length telescopes. The inside diameter is what actually limits the light (a slight fib, see Note 1), and it is a bit less that the outside diameter. We'll use 24mm, 31mm, and 50mm for the inside diameters of 0.965", 1.25", and 2" diameter eyepieces, respectively.
For the moment let's put off the question of which size to choose and explore a little on fields of view. The actual area of the sky you see when looking into the telescope/eyepiece combination is called the True field of view, or Tfov. However, optical designers can make this area appear wider or narrower, and the width as you look at it is called the apparent field of view, or Afov. This is a lot like watching television on a 10" or a 27" set. Both present exactly the same television show (same Tfov), but it appears larger on the 27" set (bigger Afov). We can relate both fields of view and the magnification in one simple relationship:
Afov = (F/f) * Tfov where: Afov is the apparent field of view, in degrees Tfov is the true field of view, in degrees F/f is the magnification (Small fib here, too. See Note 2)
Optics also tells us that the maximum Tfov, or Tmax, for any given telescope is set by the eyepiece's diameter and the telescope's focal length:
Tmax = 57.32 * D/F where: D is the eyepiece's diameter in millimeters F is the scope's focal length in millimeters 57.32 is a conversion factor that makes Tmax read in degrees. (Another fib. See Note 3)
So, if we know our scope's focal length, we can rapidly figure out what the maximum true field is for any eyepiece diameter. For this example, let's use a telescope with a focal length of 1220mm. This means that 1.25" (31mm) diameter eyepieces can never show more than 1.46 degrees of sky (57.32 times 31 divided by 1220 is 1.46), and 2" (50mm) eyepieces are limited to no more than 2.35 degrees. We use this to see whether any given eyepiece makes sense by comparing its Tfov to Tmax. If the computed Tfov is larger than Tmax, the light from the outer part of the field of view doesn't reach your eye and is wasted. Let's run some examples.
After finding an eyepiece with the maximum Tfov that is useful in your telescope, you know the bottom of your magnification range. Simply divide your scope's focal length by that eyepiece's focal length, since magnification = F/f = Afov/Tfov.
Let's go back to that question of which size of eyepiece to choose. Your telescope may limit the choice; it may be designed to work with or have a narrow exit tube that only allows some of the sizes to fit. If you are going to go up in size, then you should check to make sure the wider diameter eyepieces are neither mechanically incompatible nor vignetted by the telescope tube (if so, you won't get any increase in field of view). Otherwise, the choice boils down to the maximum field of view we want to have through the scope. If you don't care about wide views or have a short focal length scope, then smaller diameter eyepieces will be just fine. If you love big wide views and/or your scope has a very long focal length, then you'll need the bigger diameter ones. Here's a little table that shows the Tmax in degrees for all three common eyepiece diameters and a number of telescope focal lengths. If your scope's exact focal length isn't in the table, its Tmax won't be very far from the Tmax of the focal length just above or below yours:
Telescope Max True Field (Tmax) in Degrees Focal for Eyepiece Diameters of: Length 0.965" 1.25" 2" ------------------------------------------------- 400mm 3.4 4.4 7.2 500 2.8 3.6 5.7 600 2.3 3.0 4.8 700 2.0 2.5 4.1 800 1.7 2.2 3.6 (the table was computed 900 1.5 2.0 3.2 using the formula 1000 1.4 1.8 2.9 found in Note 2) 1200 1.1 1.5 2.4 1400 1.0 1.3 2.0 1600 0.9 1.1 1.8 For comparison, the full 1800 0.8 1.0 1.6 moon spreads across just 2000 0.7 0.9 1.4 about 0.5 degrees of sky. 2200 0.6 0.8 1.3 2400 0.6 0.7 1.2 2600 0.5 0.7 1.1 2800 0.5 0.6 1.0
Choose the eyepiece diameter that gives you the field of view you want to have.
Now let's get a handle on the upper magnification limit. This one is set by either the atmosphere or the aperture of the telescope. Both of these cause irreducible 'fuzz' in the image. There is no sense going too high in magni- fication because you get to the point where all you do is make the 'fuzz' bigger but gain no additional detail. The atmospheric unsteadiness, called 'seeing', varies from night to night and place to place, but usually limits us to using magnifications below something like 220-250X. You will sometimes be able to go up to 300X, but only rarely beyond that. Smaller telescopes also tend to run into their diffraction limit. This is set by the size of the aperture, and the Rule of Thumb is to disallow magnifying beyond 2.0 to 2.4 times the aperture expressed in millimeters (50-60 times the aperture in inches). That is, a 102mm (4 inch) aperture scope is going to have around 204X-245X maximum magnification. I should mention that this Rule of Thumb is subject to argument and is dependent on the viewer's personal feeling of what is sharp and what isn't; people also differ in visual acuity.
OK, so now we have a lower limit and an upper limit. It remains to fill in the middle. When you are taking out one eyepiece and putting in another, you can more easily lose track of the object you're looking at if you make too big a jump in magnification. Try to set up your eyepieces so that from one to the next there is no more than a 2 to 1 difference in magnification at the lower end of the range, and no more than about 1.5 to 1 at the upper end (control is touchier at high mag.). This is a practical limit. If you are very skilled in centering things and have a rock-solid mount that doesn't jiggle or shake at all when you switch eyepieces, then you can spread these ratios out.
A word of caution: this method assumes that the Afov of all the eyepieces are similar. If they're not, you have to use Tfov as the factor to ratio at 2:1 or 1.5:1 from eyepiece to eyepiece, rather than magnification. This takes a little more computation but the idea is otherwise the same.
Observing habits do differ, but you will probably end up doing most of your observing in the 50X to 200X magnification range. Guide your selection somewhat to have at least a couple of magnifications in that range.
Let's do an example using a 203mm aperture scope with a 2032mm focal length. Maximum magnification will rarely be over 300X because of the fact that the scope will be used in a city whose rising heat plume degrades seeing. Wanting the maximum field of view, we use 2" eyepieces for the low magni- fications. Looking in the table for 2" diameter and 2000mm, Tmax for this scope is about 1.4 degrees. Looking at the available 2" eyepieces for lower magnification, we find a 55mm, 50 degree Afov unit with a Tfov of 1.4 degrees, just at the Tmax limit. Thus the lowest magnification is set at 2032/55 or 37X. The upper limit is set by the atmosphere; 2032mm/300X is roughly 7, so the highest magnification eyepiece will be a 7mm unit that gives 290X (just under the nominal 300X limit). To fill in the middle, we expect to go down by a factor of 1.5 from the 7mm, which means an 11mm eyepiece, and up by a factor of 2 from the 55mm, to about a 27mm eyepiece. There's a more than 2:1 magnification gap between the 27mm (75X) and 11mm (185X), so maybe we will put in a fifth eyepiece and narrow all the ratios down, or maybe leave it at 4 eyepieces and try to select focal lengths to even the gaps [say 22mm (92X) and 12mm (169X) instead of 27mm and 11mm]. The exact focal lengths you compute are often not sold, and there will be other factors to consider, so you will have to have some flexibility.
Wow, sounds like you're done, but...there are those "other factors" still lurking about. While the basic scheme above will not change, these consider- ations can affect your choice of eyepieces: parfocality, weight, eye relief, exit pupil, Afov, Barlow lenses, contrast, and the shadow cast by a secondary mirror.
Magnification How Achieved Equiv. Focal Length --------------------------------------------------------------- 305X 8mm eyepiece, 2X Barlow 4mm 203X 12mm eyepiece, 2X Barlow 6mm 153X 8mm eyepiece 8mm 102X 12mm eyepiece 12mm 76X 32mm eyepiece, 2X Barlow 16mm 38X 32mm eyepiece 32mm
What about faults like internal reflections, coma, aberrations, and so forth? Eyepieces can have any or all of these, just like any other optical device. There are good designs that are well made, good designs cheaply made, and poor designs. The only way you can really tell if any particular unit is good enough to your eye is to use it and see for yourself. That's why comparing eyepieces is one of the general amusements among amateur astronomers at star parties. Eyepieces are quite a competitive business, and generally quality scales with price. Most if not all name-brand eyepieces have pretty good performance at the center of the image. As you go up in price, this "sweet spot" increases as a percentage of the total area in view. In addition, more money tends to buy more features: better baffling/blackening, more and better lens coatings, larger Afov, more eye relief, and parfocality.
When you go off to discuss eyepieces, either with other amateur astro- nomers, or with salespeople, you run into a welter of oddball names. The naming of eyepieces seems to follow no consistent pattern. Some are known the person who invented their optical design: Erfle, Plossl, Ramsden, Huygens, Nagler. Some are described after a feature of their design: orthoscopic (i.e. to have a flat field), panoptic (alluding to the wide field of view), super-wide (again, wide field), ultra-wide (yet again, wide field). Some have a series name hung on them by the maker or seller: LV, XL, LE, ultima, ultrascopic, 3000, 4000. So if you're confused about the names, it's not your fault. They really don't make a lot of sense, nor do they really matter much. An eyepiece by any name still has its:
Focal Length Apparent Field of View Eye Relief Weight Diameter Parfocal (or not) with others Price Optical Quality (sharpness, lack of aberrations, etc)
These are what you need to keep in mind when working out what eyepieces are best for you. Note that a lot of them require a use test. Will the weight unbalance your scope? Did you check to see if they were really parfocal? Is the optical quality high enough for you? These questions (and others) can only be answered by using the candidate eyepieces on your scope. Here's where other amateur astronomers can be a great help; many kinds and sizes of eyepieces are usually found at observing sessions and normally the owners don't mind helping you evaluate some.
That's the end of the lecture. Good luck choosing your eyepieces!