Caption: A diagram of a Schmidt-Cassegrain telescope, a classic reflector telescope.
The Celestron C8 telescope is an example of popular Schmidt-Cassegrain telescope. It has an 8-inch primary as its name implies.
Features:
The Schmidt corrector plate makes the telescope a SCHMIDT TELESCOPE.
Note that unlike most telescopes, the primary is NOT the first optical device in the formation of the observed image: Schmidt corrector plate is.
In a sense, the Schmidt corrector plate is the "real primary" since its area must be about the same as the primary's in order for the primary to have its full light-gathering power.
Why have a correction for spherical aberration?
Two reasons:
This is because inner and outer spherical surfaces rubbed together any which way to smooth them tend to become more and more exactly spherical. NO other curved shape allows for such a simple procedure for exact shaping. Of course, two flat surfaces rubbed together can be smoothed to greater flatness.
The diameter of the primary is the main parameter of any telescope. It is the first parameter anyone should know or ask about.
The reason for this is that the light-gathering power of a telescope is proportional to the area of the primary, and thus square of the diameter.
The primary gathers the light from the observed object (e.g., an astronomical object).
The primary usually starts the process of image formation, but in the case of the Schmidt-Cassegrain telescope where the Schmidt corrector plate does.
In general, when a telescope has a secondary, the secondary is used to create a real image that is viewed by an eyepiece.
A Schmidt-Cassegrain telescope is a CASSEGRAIN TELESCOPE because the secondary is a convex mirror is on the main optical axis of the telescope and creates the real image behind the primary---which is often a convenient place to have it.
The secondary in the Schmidt-Cassegrain telescope is embedded in the Schmidt corrector plate at the front of the Schmidt-Cassegrain telescope as shown in the diagram.
The convex mirror (usually a spherical mirror) gives a Cassegrain telescope an effective focal length longer than the focal length of the primary.
The longer effective focal length allows greater telescope magnification than otherwise, and so allows for a compact long focal-length telescope. For example, the Celestron C8 telescope (which is a Schmidt-Cassegrain telescope as aforesaid) has a telescope tube length of about 400 mm, but the effective focal length is 2032 mm = 80 inches (see Wikipedia: Celestron: Products).
The secondary gives the longer effective focal length by decreasing the angles the light rays have with respect to the optical axis. The angles then act as if they came from a longer focal-length primary.
If there were no secondary, the real image would form in somewhere front of the primary where it would be very awkward to view in visual astronomy.
Actually, large, professional telescopes are almost never used for visual astronomy, and so almost always have NO eyepiece setup. A CCD camera is usually put on the focal plane. The CCD camera records the real image.
But the diagram shows (with some close looking and imagination) how light rays from every part of a distant object make it to the real image, and so the image is complete.
But we can say a bit more:
Since the telescope aperture is circular, the beam group cross section would be circular image for a point light source if the secondary were transparent to incoming light rays.
If you have an extended object, each point on it is a point light source.
So an out of focus telescope gives a continuum of overlapping donut unfocused images.
Formally, unfocused image formation is called defocus aberration. One usually just calls an unfocused image an unfocused image or an out-of-focus image or a blurred image.
The minus sign just means that the image is point inverted and can be dropped if the point inversion is considered to be understood. Using a star diagonal usually adds a axis reflection to the image.
How the limit on FOV arises:
So you just see nothing at angles too far off the optical axis
You don't usually want to look at such large angles when comfortably doing visual astronomy.
Also Gaussian optics breaks down for sufficiently large angles and you would see some sort of distorted image.
Objects sufficiently far away that the light rays from them are effectively parallel are said to be at optical infinity. in optics jargon
By focusing, objects at less than optical infinity can be focused, but how close they can be depends on your focusing setup.
For example for C8 telescopes, focusing for a distance less than the length/width an ordinary classroom is NOT possible.