Reflecting telescopes use mirrors to gather light from distant objects. The light bounces off a large concave mirror that focuses the light on a secondary mirror. There are several types of foci, but the Coude' is quite common and is shown in our illustration below.
This type of telescope is commonly used in astronomy because it is much easier to create a large convex mirror than to create the huge lenses that would be necessary to gather the light to see dim far-away objects. The Coude' focus uses two extra mirrors to reflect the image outside of the telescope so that it can be seen through a lens or photographed.
As you can see by following the dotted red lines in our diagram, there is quite a bit of bouncing around of light rays. This means that the mirrors must be precisely made and precisely positioned in order for the telescope to work properly.
The reflecting telescope was invented not long after the refracting telescope (1672). Later, in the 1930s, another type of telescope called the "catadioptric system" was put to use at some observatories. It uses both mirrors and lenses to try to optimize viewing.
As can be inferred from our diagram, the bigger the mirror, the more light that can be focused, the brighter the image. Also, the bigger the telescope, the easier it is to distinguish two objects. As noted before, the actual magnification of the object is dependent largely on the eye-piece, but its effective clarity is again dependent on the size of the scope. Telescopes used for astronomy permanently situated at observatories are mounted on moving platforms to compensate for the Earth's motion. Amateur astronomers, unless they have a motorized mount with a computer, will be required to continually move their scope in order to keep a star or planet in their field of vision.
Another type of telescope, though not based on gathering light rays, is called the radio telescope.