# Telescope Numbers

Focal length?  Field of view?  Exit pupil?  What's it all mean?

Let's see if we can explain...

Telescopes come in many different sizes.  Likewise, so do eyepieces.  One of the first things people are usually surprised about is that telescopes don't have a fixed magnification.  Unlike binoculars, which have a single magnification, telescope eyepieces can be swapped.

Each eyepiece has a focal length (a number followed by "mm" is usually stamped on the eyepiece.)  Likewise, each telescope has a focal length,  as well as an aperture and a focal ratio.

The focal length is the distance from the primary mirror (or objective lens, for refractors) to the focal point (which is also called the prime focus).  The focal point is where the light rays converge.

The aperture of a telescope is the diameter of the primary mirror or objective lens.

The focal ratio (the number following the "f/") is merely the focal length of the telescope divided by the aperture.  So, the focal length is equal to the aperture times the focal ratio.

The one confusing item in this is that sometimes sizes are expressed in inches, and other times in millimeters.

To convert back and forth, remember that there are 2.54 centimeters to an inch.  And, there are 10 millimeters in one centimeter.  So, to convert from millimeters (mm) to inches, divide the mm by 25.4.  To convert from inches to millimeters, multiply the number of inches by 25.4.

So, here is your test.  What would the focal ratio be for a telescope with an 8 inch mirror, and a focal length of 1200 mm?

#### Magnification and Focal Length

As we've said, both telescopes and eyepieces have a "focal length".  Magnification is a measure of the number of times the image is enlarged.  A pair of 7 power binoculars magnifies the image 7 times.

To find the magnification for a particular eyepiece in your telescope, first find the focal length of the eyepiece.  This is probably stamped on the eyepiece, or the available sizes are listed in astronomy catalogs.  Second, find the focal length of the telescope.

Magnification is the focal length of the telescope divided by the focal length of the eyepiece (use the same units, if the eyepiece is specified in mm, then make sure the telescope focal length is also expressed in mm).  If you don't know the focal length of the telescope, it is equal to the focal ratio times the aperture.

For example, a 26mm eyepiece, placed in a telescope with a focal length of 1200 mm, will have a magnification of about 46x (which is 1200 / 26).  The same eyepiece, placed in a telescope with a focal length of 1430 mm will have a magnification of 55x (which is 1430 / 26).

Notice that the longer the focal length of the telescope, the greater the magnification from a given eyepiece.

You may hear a rule that says that the maximum usable magnification is 50x or 60x per inch of aperture.  This is a rough guideline, and it can vary depending on the kind of telescope you have, the seeing conditions, and what kind of object you are trying to view.  But, in general, extremely high magnifications are not useful.

#### Exit Pupil

The exit pupil is the diameter of the light beam that exits an eyepiece.

The pupil of a human eye dilates to about 7 mm when accustomed to darkness.  This varies a little from person to person, and shrinks a little with age.

If the exit pupil is greater than 7 mm, then some of the light will be lost, and the eye will not be able to take it all in.  This can be a problem when viewing from an urban or light polluted sight -- the eyepiece is not only transmitting star light, but also sky glow.  On the other hand, very small exit pupils are only good for some types of astronomical targets.  For example, an exit pupil of about 1 mm might be OK for splitting a double star, but it wouldn't be good for viewing a dim galaxy.

To find the exit pupil, divide the aperture of the telescope  (in mm) by the magnification.

Or, the exit pupil is also equal to the focal length of the eyepiece (in mm) divided by the focal ratio of the telescope (the f number).

#### Field of View

Most eyepieces list an "apparent field of view".  These range from a narrow field of around 30 degrees to a wide field of 60 to even 80 degrees or more (for example, TeleVue Naglers have an 82 degree field).  How does this translate into what you will actually see when you look through the eyepiece?

Field of view is measured in degrees, which is the same way that we gauge angular distance in the sky.

The apparent field of view is the view through the eyepiece alone.  The apparent field of a 50 degree eyepiece is bigger than the field of a 30 degree eyepiece.  If the apparent field is large, the true field is also comparatively larger than an eyepiece of the same focal length with a smaller apparent field.

The "true field of view" is approximately equal to the apparent field divided by the magnification.

For example, a 26mm Plossl with a 50 degree field of view, placed in a telescope with a focal length of 1200 mm, will have a magnification of about 46x (which is 1200 / 26), and a true field of view of just over 1 degree (1.09 degrees, which is 50 / 46).

The same 26mm Plossl eyepiece, placed in a telescope with a focal length of 2032 mm, would have a magnification of 78x, and a true field of view of 0.64 degrees.

So, what does that number mean?  How do you know how much of the sky you can see through a true field of view?

Amateur astronomers use several handy techniques to determine distances in the sky.

If your telescope is equipped with a Telrad finder, the three rings in the bullseye pattern you see through it are 0.5 degree, 2 degrees, and 4 degrees in diameter.

The distance between the two pointer stars in the end of the Big Dipper is about 5 degrees.

A fist, held at arm's length, is about 10 degrees wide.  Three fingers at arms length, are about 5 degrees wide.

The full moon is about a half a degree wide.

Now you should have an idea of what all those numbers on telescopes and eyepieces mean, and how to calculate things like magnification and exit pupil!

The mirror has a diameter of 8 inches or 203 mm.  1200 divided by 203 is 5.9, so the telescope would be an f/5.9.

Did you get it right?

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