From Nick Greene,
Your Guide to Space / Astronomy.
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Also, check out our Six Things To Know About How To Buy a Scope for Telescope Astronomy

Telescopes come in three basic designs; Refractor, Reflector, and Catadioptric.

Refractor
A refractor uses two lenses. At one end (the end farther away from the viewer), is the larger lens, called the objective lens or object glass. On the other end is the lens you look through. It is called the ocular or eyepiece.

The objective collects light and focuses it as a sharp image. This image is magnified and seen through the ocular. The eyepiece is adjusted by sliding it in and out of the telescope body to focus the image.

Reflector
A reflector works a bit differently. Light is gathered at the bottom of the scope by a concave mirror, called the Primary. The primary has a parabolic shape. There are several ways the primary can focus the light, and how it is done determines the type of reflecting telescope.

Many observatory telescopes use a photographic plate to focus the image. Called the Prime Focus Position, the plate is located near the top of the scope. Other scopes use a secondary mirror, placed in a similar position as the photographic plate, to reflect the image back down the body of the scope, where it is viewed through a hole in the primary mirror. This is known as a Cassegrain focus. (More on this later.)

Newtonian
Then, there's the Newtonian, a kind of reflector. So named because Sir Isaac Newton created the basic design. In a Newtonian, a flat mirror is placed at an angle in the same position as the secondary mirror in a Cassegrain. This secondary mirror focuses the image into an eyepiece located in the side of the tube, near the top of the scope.

Catadioptric
Finally, there are catadioptric telescopes, which combine elements of refractors and reflectors in their design.

The first such telescope was created by German astronomer Bernhard Schmidt in 1930. It used a primary mirror at the back of the telescope with a glass corrector plate in the front of the telescope, which was designed to remove spherical aberration. In the original telescope, photographic film was placed at the prime focus. There were no secondary mirror or eyepieces. The descendant of that original design, called the Schmidt-Cassegrain design, is the most popular type of telescope. Invented in the 1960s, it has a secondary mirror that bounces light through a hole in the primary mirror to an eyepiece.

Our second style of catadioptric telescope was invented by a Russian astronomer, D. Maksutov. (A Dutch astronomer, A. Bouwers, created a similar design in 1941, before Maksutov.) In the Maksutov telescope, a more spherical corrector lens than in the Schmidt is utilized. Otherwise, the designs are quite similar. Today’s models are known as Maksutov –Cassegrain.

Refractor Telescope Advantages and Disadvantages
After initial alignment, refractor optics are more resistant to misalignment. The glass surfaces are sealed inside the tube and rarely need cleaning. The sealing also minimizes affects from air currents, providing steadier sharper images. Disadvantages include a number of possible aberrations of the lenses. Also, since lenses need edge supported, this limits the size of any refractor.

Reflector Telescope Advantages and Disadvantages
Reflectors do not suffer from chromatic aberration. Mirrors are easier to build without defects than lenses, since only one side of a mirror is used. Also, because the support for a mirror is from the back, very large mirrors can be built, making larger scopes. The disadvantages include easiness of misalignment, need for frequent cleaning, and possible spherical aberration.