There are a flood of eyepieces of various designs on the amateur astronomical supply market which you can use for your own observing. You will hear strange-sounding names, terms such as field of view, focal length, exit pupil and then still not really know which eyepiece is it the right one for your observing. In order to remedy this somewhat, I have listed the various designs with their advantages and disadvantages below.
 
Basically, eyepieces are like a magnifying glass used to magnify the view of the intermediate image produced by the telescope itself. In principle, such an ‘eyepiece magnifier’ could consist of just a single lens element. Since however different eyepieces also want to produce different fields of view, an eyepiece has a combination of lens elements at various fixed spacings. But achieving longer eye relief and the correction of image aberrations are also reasons for this. The ‘holder’ which keeps all these lens elements in place is also known as the eyepiece ‘barrel’.

Huygens eyepieces

These eyepieces are a simple two lens element design which provides a relatively small apparent field of view. The lenses are not cemented together and therefore well suited for solar projection through a telescope. These eyepieces are among the oldest designs and are only rarely found among telescopes accessories. Their field of view is about 40°.

Kellner eyepieces

Kellner eyepieces are composed of three lens elements and have a field of view of around 45°. Since the two eye lenses are cemented and constitute an achromatic doublet, only a little chromatic aberration is produced. Kellner eyepieces can be used for higher magnifications with telescopes having an aperture ratio of up to 1:10. The limit with Newtonian reflectors is at an aperture ratio of 1:5, and here it is better to resort to Ploessl eyepieces.

Orthoscopic eyepieces

These eyepieces have four lens elements, two of which are biconvex and one is biconcave. These eyepieces provide a high level of sharpness both at the centre as well as at the edge of the field of view. They are therefore also of interest for planetary and double star observing. They feature a flat image field. The low absorption exhibited by these lenses due to their use of only a few lens elements and accordingly good lens coatings is another plus for these eyepieces. Their field of view is about 40° to 45°. 

Ploessl eyepieces

Ploessl eyepieces are the astronomical standard lens and anyone who does not want to spend a lot can afford these eyepieces. Often one finds these Ploessl design lenses in complete accessories kits for beginners.
These eyepieces always consist of four lens elements in two pairs. These lens element pairs are cemented together and each form an achromatic doublet meaning there is virtually no chromatic aberration. But short focal length Ploessl eyepieces have a problem with their eye relief. This means that the eye lens elements are so small that you have to position your eye very closely to the eyepiece. Your eye is glued to the eyepiece, so to speak. Other eyepiece designs are therefore preferable at short focal lengths.
Their apparent field of view is about 50°.

Super Plossl eyepieces examples of 52 ° field of view.

Erfle

You cannot find Erfle eyepieces in modern accessory catalogues as this type is no longer directly available. However, many eyepieces can be found among astronomical accessories that have the basic features of this design. Many modern eyepieces are actually a development of the Erfle design.
Erfle eyepieces have five lens elements and apparent fields of view of up to 68°. They are especially useful for use as wide-field long focal lengths eyepieces. The eye relief is not optimal at shorter focal lengths and they are therefore not recommended under 20mm.

Long eye relief eyepieces

These eyepieces have become especially popular in recent years. If you look at the eyepieces used by any amateur astronomer, you will probably find at least one of this type. These eyepieces cannot be assigned to any one particular design, but rather have long eye relief as a dominant feature.
They always have long eye relief of around 16-20mm, even at short focal lengths, and are hence especially comfortable to use.
These eyepieces are ideal for spectacle wearers, but also people who do not wear glasses appreciate the benefits

Ultra Wide Angle eyepieces example 

Nagler

Nagler eyepieces are an in-house development from the eyepiece manufacturer TeleVue. The main elements of these eyepieces consist of a number cemented doublets. Most of these eyepieces have seven lens elements, but there are also variations using fewer elements. These eyepieces you provide one with a fantastic impression of the night sky. They almost make you feel as if you are floating in space. This is due largely to their enormous apparent field of view of 80°.
These eyepieces also reduce image errors such as coma and distortion. In practice, this means that you observe sharp stars right out to the edge of the fields of view, even in ‘fast’ telescopes.

2 inch eyepieces 

Are you perhaps currently thinking of buying a telescope? Then you should also consider one with a 2" focuser, as this could give you a completely new perspective on the night sky. Or does perhaps your telescope already have a 2" focuser?
So far, we have only discussed 1.25" eyepieces - eyepieces that fit into any telescope. But with somewhat larger telescopes, from apertures of around 150mm, you also find 2" focusers fitted. But what are the benefits of 2" eyepieces?
Firstly, these eyepieces are significantly larger and heavier than their smaller 1.25" relatives. But the key feature is their much larger field stop, which does not limit the light bundle to the same extent as the smaller eyepieces hence allowing a much larger field of view. This means you can even find 2" eyepieces providing a more than a 100° apparent field of view. Observing though such an eyepiece seems limitless; it appears as if there is simply no end to the star-speckled blackness. Only when you move your eye will you eventually reach the edge of the field of view. Another advantage of these eyepieces is their very comfortable viewing, with the huge eye lens ensuring very relaxed observing.
For which objects are 2" eyepieces suitable?
In general, the longer focal length 2" eyepieces are of most interest - for example in the range 20-40mm. At the telescope, this will give you low magnifications and very wide fields of view. This makes these eyepieces especially interesting for deep sky observing. So observing faint galaxies or extended nebulae with 2" eyepieces is a real joy. But there is an additional benefit: Imagine you want to find a particular galaxy with your telescope. Despite your finderscope, you are not sure if it is actually in the field of view because you simply cannot see the faint galaxy with your naked eye. Luckily, you are now using your 2" wide angle eyepiece, covering perhaps two degrees (that is four full moon diameters!) of the night sky. Thanks to the wide field of view, you can see the galaxy directly in the eyepiece and can now set the galaxy in the centre of its field of view. 

Examples for 2 "eyepieces

Field of view

The field of view which can be achieved with an eyepiece is a crucial factor. If you look at the eyepieces available today, you will find fields of view ranging from 45° to 110°.

Here, this means the ‘apparent field of view’ (AFOV) of the eyepiece - that is the angle that can be seen by means of the eyepiece. But these large fields of view can be misleading. This is because the AFOV is very far from the field of view that you can actually see in the sky.

A very important criterion here is the telescope used. Different actual or true fields of view (TFOV) will be achieved, depending on the magnification used. If you know the AFOV of the eyepiece, then you can relatively easily calculate TFOV in the sky.

The magnification of the eyepiece in the telescope:
M = focal length of telescope / focal length of eyepiece

Example: You use a telescope with a 1000mm focal length and a 10mm eyepiece. 1000mm/10mm = 100X magnification

Calculation of the true field of view (TFOV):
TFOV = AFOV / magnification

As an example we take a Super Ploessl eyepiece with 52° AFOV:
TFOV = 52°/100X = 0.52° = ~30'

The field of view in the sky now has a size of 0.5° or *30 arc-minutes.
For comparison, the moon has a diameter of ~30 arc-minutes.

For comparison, here is a table with the different fields of view:

How do you calculate the AFOV of an eyepiece if it is not provided?

Measure the diameter of the field stop at the bottom of the eyepiece. To do this, unscrew the eyepiece barrel, allowing you to easily determine the diameter of the free passage of light. The second value you need is the focal length, which can be found printed on the eyepiece. The following inverse tangent function allows you to calculate the AFOV:

AFOV = half the field stop diameter / eyepiece focal length tan-1

Not the whole field stop, but only half is used.
The result is then multiplied by 2.

Example:
I measure a field stop of 12mm with a 12.5mm focal length Ploessl eyepiece. These two pieces of information are now put into the formula with, however, only half the diameter of the field stop, i.e. 6mm:

6mm/12.5mm tan-1 = 25.6 x 2 = 51°

Spoilt for choice, which eyepiece suits my telescope?

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