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Eyepieces determine the magnification and
field of view of a telescope.
Different eyepieces are used to view different objects. Some objects, such
as nebulae and star clusters, appear quite large and are best viewed at low
magnifications (which give a wider field of view), whereas planets appear very
small and are normally viewed with high-magnification eyepieces. One of
the most common misconceptions in amateur astronomy is that magnification is the
most important aspect of a telescope. In reality, the diameter (aperture)
of a telescope determines its power and different eyepieces are used to get the
best view of a given object. Often the best view is at a low
magnification. Be sure to read the section on
Understanding Magnification
for more details.
How Eyepieces Work
Why are eyepieces even necessary? A telescope is an optical system that
creates an image, just like a camera lens creates an image on film. In
fact, placing a camera at the focus of a telescope will also capture an image,
since the telescope becomes the camera lens. But, placing your eye at the
focus point of a telescope does not produce an image. Why not?
Because your eye is also an optical system. Your eye focuses light just
like a telescope does, and it cannot focus on a real image such as that
created by a telescope. It requires a virtual image, which is what
an eyepiece creates.
Take a look at the diagram below. It shows that both a telescope and
your eye focus light to a point. Placing an eyepiece at the focal point of
a telescope then creates a light beam which is neither converging nor diverging.
Your eye can then focus the light beam exiting the eyepiece.

Above: How an optical system consisting of a telescope,
eyepiece, and eye creates a final image
Magnification
The most important eyepiece characteristic is
focal length. This is the
number, in millimeters, written on the side of every eyepiece. It allows
you to determine the magnification an eyepiece gives in combination with a
given telescope. Magnification is determined simply by dividing the focal
length of the telescope by the focal length of the eyepiece.

This means that a smaller number on an eyepiece gives a higher magnification.
A 10mm eyepiece would provide twice as much magnification as a 20mm eyepiece.
It also means that the same eyepiece gives different magnifications on different
scopes. A 10mm eyepiece would be low power on a short-focal-length scope
but high power on a long-focal-length scope. For example, on an 80mm
short-focal-length refractor, a
10mm might only provide 40x magnification, but the same eyepiece on a 10"
Schmidt-Cassegrain telescope would give 300x.
A typical eyepiece collection would include 3 eyepieces: one low power,
one medium power, and one high power. The usual magnification range
depends on the telescope, but for most scopes the normal range might be from 50x
to 250x.

Above: Increasing the magnification makes the image larger,
but the image gets dimmer and the field of view gets smaller
Eye Relief
This is an important aspect of many eyepieces. Eye relief is the
distance from the eyepiece to the observer's eye. The shorter this
distance, the more difficult it can be to observe. Also, if the observer
must wear eyeglasses, short-eye-relief eyepieces can be very difficult or
impossible to use. Long-focal-length eyepieces (usually low power)
inherently have long eye relief, so they do not need to be specially designed to
increase eye relief. Short-focal-length eyepieces (usually high power), on
the other hand, do not inherently have long eye relief and must be specially
designed to make them easier to use.

Above: The eye relief of an eyepiece is the distance from the top lens
in the eyepiece to the observer's eye

Above: Two short focal length eyepieces, one with normal eye
relief and one specially designed with long eye relief. Note the
difference in the size of the eye lens.
Field of View
The amount of sky seen through an eyepiece (called the
true field of view) is
determined by both the magnification and the eyepiece's
apparent field of view.
Apparent field of view is a design characteristic of an eyepiece design.
Some eyepieces have narrow apparent fields and some have wide apparent fields.
If the magnification is kept the same (i.e., the eyepieces have the same focal
length), an eyepiece with a wider apparent field will have a wider true field.

Above: Changing the apparent field but not the magnification
changes the field of view but not the object size
You can also change field of view by simply changing magnification. If
the apparent field is kept the same, a lower power eyepiece will give a wider
field of view. To view very large objects such as the Andromeda Galaxy or
Pleiades star cluster, you need a very large field of view and hence a very low
magnification. Field of view is very important for getting the best view.

Above: Increasing the magnification may not always result in
a better view, especially if the object being viewed is very large
Eyepiece Sizes
There are two standard sizes of telescope eyepieces. The sizes are
determined by the diameter of the eyepiece barrel that fits into the telescope.
The two standard sizes are 1.25" and 2". A third size, 0.965", is a
smaller standard that is usually best to avoid (see below).
1.25" Eyepieces
Almost all telescopes are designed to be used with 1.25" diameter eyepieces.
Most telescopes will include at least one 1.25" eyepiece. Accessories such
as Barlow lenses and filters are designed to thread into the barrel of these
eyepieces, so such accessories are also distinguished by size. Good 1.25"
eyepieces typically cost $40-200, although there are more and less expensive
models.
2" Eyepieces
The second standard size is the larger 2" diameter. Many telescopes
will accept these eyepieces, though some telescopes will require an optional
adapter. Not all telescopes work with 2" eyepieces. 2" eyepieces are
wide-field, low-power eyepieces. Above a certain magnification (which
depends on the design), 2" diameter barrels are not required, so not all
wide-field eyepieces are 2"--some will still be 1.25" and this is not a
disadvantage, just a function of the design. This is a common
misconception. Accessories such as filters and Barlow lenses are designed
for 2" eyepieces as well. 2" eyepieces typically cost $200-400, with some
of the largest and highest quality eyepieces costing around $600. Some
inexpensive models are also available for around $100, though these will
obviously not have the features or quality of the more expensive eyepieces.

Above: A 2" wide-field eyepiece compared to a
standard 1.25" eyepiece. Both are 26mm eyepieces.
0.965" Eyepieces
The final eyepiece size is the one to avoid. 0.965" eyepieces are the
standard size for "department store" telescopes. These inexpensive
telescopes often frustrate new stargazers, and one of the primary
reasons is that viewing through 0.965" eyepieces is all but impossible.
Also, standard accessories such as Barlow lenses and filters are not normally
available for these eyepieces. And you are usually stuck with the
eyepieces that come with the scope since 0.965" eyepieces are rarely sold
separately. The difference between a scope with 1.25" eyepieces and one
with 0.965" eyepieces is usually the difference between a scope that ends up in
the yard showing you the wonders of the universe and one that ends up in the
closet collecting dust.

Eyepieces
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