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Diagram of a Newtonian reflector telescopes showing the light path inside (thank you Wikipedia).
Real simple here. The light comes in the front of the scope goes to the primary mirror that is ground parabolic (like a bowl) that focuses the light to a secondary mirror that is set on a 90 degree angle. That, reflects the light to the bottom of your eye piece. There you have it!
Reflector telescopes are so simple they can be built on a piece of 2 x 4 lumber!
I am going to keep this basic as possible.
There many styles of reflector telescopes. So many in fact that we are not even going to attempt to go over all of them here. Just keep in mind. They are ALL still reflector telescopes! The major difference is the style which the mirrors are ground and the combination of mirrors and reflector lens.
The simplest Reflector is the Newtonian style reflector telescopes style reflector telescopes. They were invented by Sir Isaac Newton and is a very simple in design. Any one can build one with materials easy to obtain. Most of the material can be found in the scrap pile of the average garage. you can even grind your own mirror if you want.
For a "first telescope" the plain Newtonian reflector telescopes are the most versatile and flexible scopes to consider. It is also at the very top of the list for "affordable Telescopes"

This is a friends 8 inch "discovery" OTA on a dobsonian mount
That is Troy 12 yrs old running the scope at a star party in Balboa Park here in San Diego
Reflector telescopes are by far the the most popular telescope amongst amateur astronomers for many many reasons. Getting the most "bang for your buck" is the most used term. For the average amateur astronomer, this would be Newtonian "reflector telescopes" on a Dobsonian Mount commonly called a "Dobsonian Scope". Don't let the name fool you! It is a simple reflector "optical tube assembly " (OTA) on a very simple mount. The mount was invented by John Dobson founder of the San Francisco Sidewalk Astronomers I have had the pleasure of observing with John and I have heard him speak his view on cosmology a couple of times. (For more information on the Dobsonian Telescope go here)
The other very popular "First Scope" are Catadioptric Style of reflector telescopes. Very simply put the catadioptric's are reflector telescopes with glasses. They are compact, efficient and will fit on any kind of scope mounts. For a First Telescope they are a little more expensive than the dobsonian style reflector telescopes.
The advantages of the combination reflector telescopes are many! They are compact for a long focal length scope! They are usually packaged with a o-to mount, they are great for Astrophotography, you can mount your OTA on a fork mount or an equatorial mount ...(these types of reflector telescopes are not well suited for a dobsonian type telescope mount) Probably the best thing about the combination style of reflector telescopes is their corrective reflector lens!
Catadioptric's can be VERY confusing especially to the beginning amateur astronomer.
I guess the best way to explain a catadioptric telescope is to go to the name of the style telescope.
Simply, Richey Chretien reflector telescopes are telescopes with a Richey Chretien ground mirror. "Richey Chretien" is the style in with the mirror was ground and how it focuses the light to the secondary mirror.
Note: A Richey Chretien (RCT) type of primary mirror and secondary mirror system is considered one of the best telescope combinations to be had for viewing and astrophotography. They are also VERY TEMPREMENTAL. to calibrate and keep adjusted.
A Cassegrain is a different style of mirror system that has a parabolic ground primary mirror with a hole in the center that allows the light to be focused from the secondary mirror through the primary mirror to the focal point at the eyepiece.
The other name, in combination style reflector telescopes is the name of the people that designed the corrective reflector lens that is at the front of the reflector telescopes. Schmidt, is a type of reflector lens Maksutov is a type of reflector lens as is klestov and there are more designs for reflector lens that get way up there in the astro-geek world!
Remember: They are ALL reflector lens that help to correct or straighten the light path that enters the front of the reflector telescope! That gives the mirror system a head start toward operating at optimum efficiency!
Hence the Schmidt / Cassegrain is a Cassegrain mirror system with a Schmidt corrective reflector lens to straighten the light entering the OTA . The reflector lens helps the Cassegrain mirrors to work at optimum performance
The same would be true for the Maksutov / Cassegrain Combination Reflector Telescopes!
Note: A Maksutov/Cassegrain telescope is a wonderful viewing device! For visual and astrophotography, some folks say as good as a refractor and others think they are Almost as good as a refractor either is a compliment for any reflector telescopes!
I know that is a lot and may be long winded...but once you start to study these styles of reflector telescopes you will understand that it is REALLY DIFFICULT to give a simple explanation for these telescopes...If you seriously want to understand exactly how they work. Start here ...I warn you ....They are very complicated to say the least.
There are companies that put these scopes together in a myriad of combinations and sizes to suit almost every type of astronomy you can think off.
You will hear all kinds of names for what you may think are different types of telescopes. Richey Chretien, Cassegrain, Schmidt Cassegrain. Maksutov Cassegrain , Klestov Cassegrain, on and on it goes.
These are all styles of mirror grinds and combinations of mirrors and reflector lens.
They are ALL reflector telescopes!
A large mead reflector telescopes on an equatorial mount

He had a camera in the eyepiece hooked up to his computer so the star party public could see some great pics of Jupiter. 9-3-08
Balboa Park Star Party in San Diego

Jupiter on computer from reflector telescopes above

Catadioptric reflector telescopes are commonly matched with fork type mounts scope and mount pairing is important. Note the glass on the front of the scope. That is the reflector lens! In this case it is a Schmidt reflector lens with a Cassegrain Mirror system...
Schmidt/Cassegrain telescope or SCT for short
Remember: The Newtonian and the Catadioptric are both "reflector telescopes" the catadioptric always has a reflector lens! With the newtonian telescope the reflector lens is optional!
See Refractor Telescopes next
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