A reflector (also known as a catoptric) is a type of telescope that uses a mirror as its objective to gather light and bring the observed object into focus. As with all telescope types, it can gather more light than the eye can unassisted and will allow greater detail to be observed. The main or primary mirror of a reflecting telescope has a concave curved surface which is very accurately ground to either a spherical figure, or more usually a parabolic figure allowing incoming light to be brought to a single point of focus called the focal point.
One advantage of reflecting telescopes is that they don't suffer from chromatic aberration as no refraction of light is involved. However, there are other image distortion problems that they do incur including coma where stars in the centre of the field of view are perfectly sharp pinpoints but degrade to a comet like appearance towards the edges of the field of view. They can also require regular collimation to keep their optical elements parallel and on axis.
The distance from the plane of the primary to the focal point is the focal length of the telescope and this. combined with the diameter of the primary mirror gives the focal ratio (f number) of the telescope which in turn determines its angle of view and effective speed. In simple terms, the lower the f number, the faster the telescope and the wider the field of view. The higher the f number, the slower the telescope and the narrower the field of view. The focal length of the telescope with the focal length of the eyepiece also determines the magnification available.
Simply:
Focal ratio (f number) = focal length/objective diameter
So, my 8.75 inch dobsonian has a focal length of 1295mm and an objective diameter of 222mm giving a focal ration of 1295/222 = f5.8
Whereas my 16 inch has a focal length of 1829mm and an objective diameter of 406.4mm giving a focal length of 1829/406.4 = f4.5
Note that the f number is a ratio - it's a dimensionless number and has no unit of measurement associated with it.
Now for magnification. Again, simply:
Magnification = focal length of telescope/focal length of eyepiece
So a 25mm eyepiece in my 8.75" dobsonian will give a magnification of 1295/25 = 51.8x
The same 25mm eyepiece in my 16" dobsonian will give a magnification of 1829/25 = 73.1x
There are several configurations of reflecting telescope, and these are discussed below.
Newtonian
This is the reflector that most astronomers will be familiar with. It uses either a spherical (for long focal lengths a spherical figure is acceptable on the primary) primary mirror or more typically, a parabolic primary mirror to reflect and focus incoming light and an oval optically flat secondary mirror set at 45 degrees near the top of the optical tube to bend the focused light towards the eyepiece which is set in the side of the tube. The primary mirror is held in a special mechanical cell that allows the mirror to be finely tilted in three directions to allow it to be correctly aligned with the secondary. The secondary mirror and its holder is suspended in the tube by a spider consisting of 1, 2, 3 or 4 very thin arms that pass through holes in the body of the tube and secured with nuts. The secondary can be rotated in the tube and adjusted for height if necessary and also be tilted in three directions to allow it to be aligned with both focuser and primary mirror. The process of alignment is called collimation and is covered in a separate article. It's a very simple design and is relatively cheap to produce. The image produced is reversed in both planes (i.e. upside-down and back-to-front).
Gregorian
This is a more unusual design and can be found in some professional instruments. It isn't used in mass produced amateur telescopes. The principle of the Gregorian is similar to the Newtonian, but instead of the secondary being optically flat and mounted at 45 degrees, it's concave and mounted parallel with respect to the primary. The reflected and focused light passes through a hole in the centre of the primary and is brought to focus in an eyepiece at the bottom end of the tube. The image produced is upright.
Cassegrain
Cassegrain telescopes are similar in design to the Gregorian reflector in that they have a secondary mirror placed parallel to the primary and reflect light through a hole in the centre of the primary. However, in the cassegrain, the primary has a parabolic figure and the secondary a hyperbolic figure.
Ritchey Chretien
The Ritchey-Chretien, usually shortened to RC, is a special type of Cassegrain that has hyperbolic primary and secondary mirrors. This design allows the image produced to be free of both coma and spherical errors. RC telescopes are particularly suited to imaging and are widely used by professional astronomers.
Nasmyth/Coude
The Nasmyth reflector is similar in design to the Cassegrain, but instead of the light being brought to focus through a hole in the primary, it uses a third, optically flat oval mirror to project the light through a hole in the side of the telescope near to the base. The Coude variant projects the light through the declination axis.
Off axis reflectors
Off axis reflectors employ a tilted primary mirror to avoid obstructing the light path by either not having to use a secondary, bringing the light to focus outside of the optical tube, or placing the secondary and subsequent elements outside of the optical tube and hence out of the incoming light path. There are a number of variations of this type of telescope, examples being the Herschelian, Yolo and Schiefspiegler.