Purpose
Eyepieces are designed to enlarge the image formed by the main mirror or the objective lens (in case of a refractor) of the telescope. The focal length of the main mirror or lens divided by the focal length of the eyepiece determines the magnification of the telescope. This means that a telescope mirror or lens with a focal length of 120 cm used with an eyepiece of focal length 2 cm will have a magnification of 60 (usually written 60X) Using the same objective or main lens with an eyepiece of 1 cm centimetre (or 10mm) focal length gives the telescope a magnification of 120X.
However, although we can increase this magnification more by reducing the eyepiece to 9mm, or even shorter the image soon deteriorates. This is because of two factors: light-gathering ability (or aperture) of the main objective and seeing conditions. It will also be noticed that the greater the magnification the smaller the field of view and the faster the object in the field slips away.
Eyepiece makers experiment in eyepiece design to overcome some of these problems: they design eyepieces with wider fields and with flatter fields right to the edge of vision or even use superior glass that allows more light through to the eye. These eyepieces can become very costly and often with little increase in image quality. All of these tactics are a compromise because more lenses are required in such eyepieces, which further reduce light.
What Eyepieces to Buy
The best eyepieces are those that suit the aperture of your telescope, its focal length and what seeing is like in your area. In most conditions two eyepieces are enough: a low power and a medium or high power. I own six eyepieces and this is my percentage usage over time: Low to Medium power (60%); (Medium to High Power (40%), High Power (20%). For my most commonly used telescope, with 200mm (8”) objective, focal length 180mm, this is a magnification of 100X and 120X. I rarely resort to higher powers and if I do I use a Barlow Lens, which is a device inserted between the eyepiece and the main objective that increases the magnification or any eyepiece by 2X or 3X. Although I have a good view of most areas of sky, I get moisture and poor seeing during more than 50% of my viewing time. Only on exceptional nights can I see sharp images using high powers. These are rare nights. At the other end of the scale some nights exist when no image at any power is crisp, not even in binoculars.
Conclusion
Test your telescope and your viewing area with a variety of borrowed eyepieces and in time you will find two or three that are best for your machine. No matter how many you eventually buy, you will be most comfortable with two eyepieces on most occasions.