The Primary Optical device is the first lens or mirror that light touches. The diameter of the Primary Optical Device is also (generally) the Aperture Diameter. The light-gathering power of a telescope depends on the area of the aperture, and so this “light-gathering power” goes with the square of the diameter or radius.

The physical or effective distance between the Primary Optical Device and the focal point is called the focal length, measured along the optical axis. Given a point-like object sufficiently far away that its light rays impinge the primary optical device as light rays parallel to each other and parallel to the optical axis, the optical system will focus the rays to the focal point. The plane perpendicular to the line containing the optical axis and the focal point is the focal plane. It is on this plane that all images are formed.

Optical systems can use lenses, mirrors, or a combination of both to focus light. Both methods of redirecting light rays to focus an observed object into an image may require more than just one lens or one mirror. In such systems, the total system is a compound system that has an effective focal length that can be intuitive in the case of using thin lenses or more mathematically obscure such as in the cases of using spheroidal/paraboloid/hyperboloid mirrors.

Refractor telescopes make use of lenses to focus light. When light strikes an interface between two media, the direction of the light ray changes according to Snell's Law. The $n$ that appears on either side of this law is called the “refractive index” and is modulated by material properties and usually depends strongly on the wavelength of the incident light. In this way, a prism can be constructed that separates a light ray of white light into a range of colors.

Due to this, images from refractors can suffer from a chromatic aberration, where the colors of light spread-out on the focal plane.

Refractor tubes must generally accommodate the entire focal length of the system. This, coupled with the desire for high light-gathering power makes the feat of engineering a long tube that holds a large lens at an end cumbersome.

Reflector telescopes make use of mirrors to focus light. When light strikes a mirror, the direction of the light ray changes according to the Law of Reflection ($\theta_i = \theta_f$; angle of incidence and angle of reflection are equal about a plane normal to the mirror surface).

In contrast to refractors, reflectors suffer from no chromatic aberration, but can suffer from spherical aberration if using spherical mirrors. This aberration owes to the spherical focal plane and is observed as a loss of focus radially from the focal point. Further, the coma aberration can smear focused light. Both of these are correctable with geometric modifications of the mirrors at manufacture-time.

Since mirrors can be arbitrarily thin (so long as they're still reflective on one side) the weight of reflectors can be much less than a similarly powered refractor. Further, the introduction of non-flat mirrors allows for the effective focal length to be reduced many times the actual number of mirrors, lending shorter tubes to reflector telescopes.

In either case, we can determine the so-called “plate scale”. This plate scale is a measure of what angle each linear piece of the focal plane can image. Consider a detector of linear size, $s$, placed along the focal plane (at the end of the focal length ($f$)). Treat this detector size as the far-leg of a right triangle and the other leg as the focal length. In general, the focal length will be much larger than the detector size, so you can employ a small angle approximation to find that the angle the detector “sees” is roughly $\frac{s}{f}[rad]$. To convert this measure from radians to arcseconds, make clever use of unit ratios :)