For an in advanced guide read this.
Every telescope has a stated focal length, which is effectively the distance from the primary lens or mirror to the point at which it forms an image of a very distant object. This is a figure that you'll usually see printed or engraved near the eyepiece focuser and usually lies in the range of 400- to 3000-mm, depending on the aperture and type of telescope.
Eyepieces have focal lengths, too, which are found printed in millimeters on the eyepiece (25mm or 10-mm, for example).
To calculate the magnification of a telescope/eyepiece combo simply divide the focal length of the scope by that of the eyepiece. A 1000-mm focal length scope used with a 25-mm eyepiece will deliver 1000/25 = 40x power. The same eyepiece used with a different focal length scope will give different powers.
A simple way to increase magnification is to use a Barlow lens in addition to your existing eyepiece. A 2x Barlow will double the magnification of any existing eyepiece.
Since longer-focal-length eyepieces generally have longer eye relief, using a Barlow to increase magnification will allow more comfortable high-power viewing.
Eyepieces come in multiple sizes: the higher the number the lower the power.
Always start with the lowest-power (highest mm) eyepiece because it is easier to focus and has a wider field-of-view. Most of your observing will be done with lower power eyepieces: the images are much brighter and crisper, providing more enjoyment of the objects you're observing.
As eyepiece power increases (mm decreases), the sharpness and detail diminishes, so higher powers are mainly used for lunar, planetary, and binary star observations.
Realistically, the atmosphere will limit your viewing to a maximum of about 300x magnification, no matter how large your telescope's aperture.
Image showing that when you get closer, the image is bigger (higher magnification) and when you get further, the image is smaller (lower magnification). Click on image for a technical explanation.
Astronomical eyepieces are described by the diameter of the base tube or barrel and come in several standard diameters. This is not to be confused with the focal length of individual eyepieces, discussed earlier. The most common size is the 1.25" eyepiece. The largest size commonly encountered is the 2" eyepiece.
The eyepiece diameter for your scope is important to know when purchasing other accessories too, such as cameras, adapters and filters - almost all accessories are available in the 1.25" size.
Like any lenses there are cheap eyepieces through and expensive (top quality) eyepieces. Your telescope is only as good as the optics of the eyepiece you’re using. Even if you have the most amazing telescope quality, but if you use a poorly manufactured eyepiece, you run the risk of wasting the full capability of your telescope. There has to be a balance between the quality of your telescope and the quality of your eyepiece.
Plössl eyepieces, using 4 or 5 elements, are a good all-rounder, particularly when anti-reflection multicoated and seems to be the most popular eyepiece design today. A Plössl can deliver well-corrected, wide fields of view with good eye relief — meaning the eye can be positioned at a comfortable distance behind the rear lens and still see the whole field of view.
You'll be choosing long and medium focal length eyepieces to "frame" the subject, and short focal length eyepieces to reach optimum contrast and resolution for viewing planets and double stars.
Observers who wear glasses to correct for simple long- or short-sightedness (no astigmatism) don't need to use them at the telescope; a twist of the focuser will remedy that.
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