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Refracting Telescope 
Refraction is the bending of light as a result of its passage from one medium to another. In a refracting telescope, a lens with curved surfaces allows light to pass from air to glass and then back to air, bending it toward the optical axis of the lens. If the surfaces of the lens are shaped properly, the light is brought to a focus so you can see the night sky clearly.
Advantages - They have a completely clear aperture. No central obstruction causes light to be scattered from brighter to darker areas, and thus they have better contrast.
- They are low maintenance. Lenses do not require re-coating like mirrors do, and the optical tube assembly of a refractor doesn't ever require realignment because it is fixed into place.
Disadvantages - Because it is a closed-tube assembly, it can require a longer amount of time to cool to ambient temperature.
- Some blurring and colour changes can occur when looking at particularly bright images.
- They carry a weighty price-tag.
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Reflecting Telescope
A reflecting telescope contains two mirrors — a large primary mirror at the bottom of the tube and a small, flat secondary mirror near the top of the tube. As light enters the tube, it strikes the primary mirror, is then reflected to the secondary mirror, and then reflected again into the eyepiece.
Advantages
- They're cheap. Because mirrors have only one optical surface--as opposed to apochromatic lenses which have between four and eight--they are much less expensive to produce.
Disadvantages - The secondary mirror can create a central obstruction that can cause some scattering of light and loss of contrast.
- They can create comas--stars at the edge of the field of view look like comets.
- Mirrors require recoating after several years.
- They are fragile.
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Catadioptric Telescope
These scopes also are known as compound telescopes and are hybrids that incorporate both refractor and reflector elements in their design. They commonly have a spherical primary mirror in the back and a glass corrector plate in the front. This telescope is used primarily for photography.
Advantages - They have a very long focal length in a very short, portable package.
- They can use a lighter mount.
Disadvantages - They are also subject to a central obstruction.
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