The four basic forms of telescope optics are shown in the figure below. Each of these has an objective that collects the light, bringing it to a focus.
Refracting telescope
An objective lens brings starlight to a focus. Subject to chromatic aberration caused by dispersion in the glass of the objective. Chromatic aberration can be compensated with a lens of several elements of differing materials.
Prime focus reflecting telescope
A (typically) parabolic objective or primary mirror reflects light back to a detector (camera or other device) at the prime focus. Telescopes with only reflecting optics are not subject to chromatic aberration
Newtonian reflecting telescope
A (typically) parabolic primary mirror reflects light to a flat secondary mirror and thence to the focus. The obstruction of the light beam caused by the secondary mirror is typically less than 10% of the total incoming light.
Cassegrain reflecting telescope
A parabolic primary reflects light to a hyperbolic secondary mirror and thence to the focus through a hole in the primary mirror. The secondary mirror has a magnification factor m yielding an effective focal length which is m times the focal length of the primary mirror. This allows a much shorter overall telescope tube length than for the other types of telescopes for the same effective focal length.

Objective Mirror
Spherical
The simplest (and easiest to make) objective mirror for a telescope is concave and spherical in cross section. For paraxial rays a spherical mirror is quite adequate. For ray further from the axis, however, spherical aberration limits the sharpness of images that can be formed.
Parabolic
A parabolic cross section fully corrects spherical aberration and parabolic mirrors are common in small and moderate aperature telescopes. A parabolic mirror does introduce other aberrations (coma, astigmatism, distortion, and curvature of field) and large modern telescopes generally have more complex surface figures to minimize specific aberrations.
Light gathering Power: Each of the telescopes shown earlier has the same aperture D and hence the same light gathering power, which is proportional to the area of the objective. For unresolved objects such as stars the speed of a telescope is proportional to its light gathering power.
F-ratio
The "f-ratio" of a telescope or camera is given by the ratio of the focal length to the aperture and is therefore defined as (F/D). For telescopes of the same aperture D the size of the image (see image scale) depends on the focal length. Doubling the focal length (and hence the f-ratio) doubles the linear size of an extended image and therefore the light is spread over four times the area. Thus the speed of a telescope for imaging extended objects is inversely proportional to the square of the f-ratio.
Image scale
If it is the image in the focal plane that is of interest (as is the case when a CCD camera is the detector) then it is image scale rather than magnification that must be calculated. The linear size of an image d of an object of angular size where theta is in radians. Image scale in mm per arc-second is s=F/206.265 if F is in meters. For a 46 cm f/10.5 telescope this works out to s= 0.023 mm/arc-second which gives an inverse scale of 43 arc-seconds per mm.
Limit of Resolution
Diffraction by a circular aperture (such as a telescope objective) results in point source being imaged as a central maximum surrounded by circular rings. Rayleigh's criterion says that the limit of resolution of a telescope when looking at a double star is given by 1.22xl/D radians (about 4.56/D arc-seconds in the visible if D is in inches). At this limit the maximum of the diffraction pattern of one star will fall on the first minimum of the other star.