A refractor (also known as a dioptric) is a telescope that uses a lens 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 object lens bends or refracts incoming parallel light and causes it to converge to a single point of focus called the focal point. Incoming non parallel light will converge on to the focal plane.
The distance from the plane of the objective lens to the focal point is the focal length of the telescope and this. combined with the diameter of the objective lens 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 Tal 100RS has a focal length of 1000mm and an objective diameter of 100mm giving a focal ration of 1000/100 = f10
Whereas my Equinox 80 has a focal length of 500mm and an objective diameter of 80mm giving a focal length of 500/80 = f6.25
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 Tal 100RS will give a magnification of 1000/25 = 40x
The same 25mm eyepiece in my Equinox 80 will give a magnification of 500/25 = 20x
Generally speaking, longer, slower telescopes like the Tal are ideally suited for planetary observation and brighter objects as their narrow field of view and high focal length allow good magnifications to be used (subject, of course, to seeing conditions), but their relatively low speed doesn't allow as much light to be brought to focus. The shorter faster telescopes like the Equinox 80 are ideally suited for larger and fainter deep space objects like nebulae as their wider field of view and low focal length give lower magnification but their faster speed allows more light to be brought to focus.
There are two principal types of reflector, achromatic and apochromatic and these are discussed below.
Achromatic.
Visible light is a tiny part of the electromagnetic spectrum and as such spans wavelengths from around 390 nanometres to around 750 nanometres. A simple lens will not be able to focus the different wavelengths of light and hence different colours to exactly the same point. Red light will focus furthest away from the lens, green somewhere in the middle and blue nearest the lens. This will show a bright subject with colour fringes as some colours will be slightly out of focus. This phenomenon is called chromatic abberation.
Very early telescopes used a single lens element for the objective and suffered very badly from this effect. The achromatic telescope has an objective lens consisting of two elements made of different types of glass (crown glass and flint glass) called a doublet. Each of the lenses bends or refracts the light in a slightly different way. The effect of this is to bring two of the colours into focus at the same point and this minimises the chromatic aberration seen. There will still be some fringing as not all of the colours will be in focus, but it is greatly reduced and only really visible with very bright objects.
Apochromatic.
An apochromatic telescope has an objective lens consisting of two (doublet) or three (triplet) elements made from a special type of glass, often containing fluorite, that reduces dispersion to a level where it really has no significant impact. The effect of this is to virtually eliminate chromatic aberration and produce a fringe free image in the eyepiece.
The cheaper apochromatic telescopes use doublet lenses and perform extremely well although under some conditions with very bright objects, some fringing may still be seen. The more expensive apochromatic telescopes use triplet lenses with the third element bringing the out of focus colour into the same focal plane as the others.