eyepiece explanation

A telescope is an optical device, usually using mirrors and lenses, which is capable of magnifying an image seen at a distance. All telescopes require at least two elements, an "objective" which collects and focuses the light, and an "eyepiece" which is used to examine the image. The telescope we're using has three optical elements: a primary curved mirror to focus the light, a secondary flat mirror to reflect the light path out the side of the telescope

Both curved mirrors and lenses have focal lengths, which is the distance from the lens at which an image will form and light rays which started out parallel will come together to a point--that is, the length from the lens to the point where the image comes into focus. To determine the "magnification" of a telescope (or how much bigger an object will appear in the telescope compared to just using your eye), we can simply divide the focal length of the telescope by the focal length of its eyepiece.

Magnification = Focal Length of Telescope / Focal Length of Eyepiece
Focal Length of Eyepiece = Focal Length of Telescope / Magnification

The telescope we're using has a focal length of 450 millimeters ("mm"), or about 18 inches. (A "meter" is a length of about 3.28 feet, and most countries other than the United States use meters to measure length instead of feet. You need one thousand millimeters to make one meter.) The telescope's focal length can not be changed, because the focal length comes from the exact shape of the mirror, and if you could bend the mirror to change its shape it would not make an image.

But we have four eyepieces, with focal lengths of 20, 15, 9, and 6 millimeters respectively. These numbers are printed on the barrels of each eyepiece. We can substitute the numbers of our eyepiece and telescope focal lengths into the formulas above:

Focal Length of Telescope / Focal Length of Eyepiece = Magnification.

Different magnifications are useful for different purposes. A low magnification is useful for finding objects, since the amount of sky you can see through the eyepiece is much larger. Also, some faint fuzzy objects like nebulae, galaxies, and star clusters, will appear brighter when seen with a lower magnification. A high magnification is useful for looking at double stars--stars which are very close together--as well as details on the Moon and planets. But you won't see as much of the sky, and the "window" you're looking through is smaller, so finding an object and keeping the telescope pointed at that object is more difficult.

You can do the division yourself to check, but the magnification you get with each eyepiece is shown below:
450mm/20mm = 22.5
450mm/15mm = 30
450mm/9mm = 50
450mm/6mm = 75

It is usually a good idea to start finding an object with a low magnification, and then when you've found and centered the object in the view, you can zoom in on it by taking out the eyepiece and replacing it with one with a shorter focal length.

But hold on. Why are the 6mm and 9mm eyepieces LONGER than the 20mm and 15mm, if they're supposed to have a shorter focal length? This is because they've got a trick up their sleeve. Usually when you use an eyepiece with a short focal length, the size of the lens goes down and you have to get your eye really close to the lens to look through, which is tough if you've got glasses on. But there is another way to get a short focal length. Some telescopes and eyepiece sets come with a special adapter lens called a "Barlow" which uses special lenses to effectively increase the focal length of the telescope itself. You can then put an eyepiece into the Barlow and the eyepiece will have a higher magnification than it would have without the Barlow. But you can also make an eyepiece where you fit the Barlow lens into the eyepiece barrel itself, so a single eyepiece can have a large lens and a high magnification. And to fit the Barlow lens inside, the eyepiece barrel has to be longer.