To make modern astronomical observations, one needs a telescope and a detector, but generally also an instrument to modify the light delivered from the telescope. The telescope brings light from near-infinity to a focus on its focal surface. For large optical/IR telescopes, the focal length at the secondary focus (Cassegrain/Gregorian/Nasmyth) is quite large, and so is the diameter of the focal surface. While it is possible to put a detector directly at the secondary focus, the sizes of modern electronic detectors are much smaller than the focal surfaces of large telescopes, and so reimaging instrumentation is used to demagnify the image. (The major exceptions are imaging cameras placed at the prime focus of the telescope.)
In order to do wide field imaging or nearly any kind of spectroscopy, we typically place a reimaging instrument behind the focal surface, and slits at the focal surface, if needed for spectroscopy. The instrument usually consists of a collimating lens, a dispersing element in the collimated beam if desired, and a camera that reimages the collimated beams onto a detector.
This document attempts to explain some basics of these reimaging systems and to derive some scaling laws. This is not an optics text. There are many existing texts, but few specifically treat astronomical applications and many optics texts drop the reader directly into complexities such as the mathematics of aberrations. For further background and more detail, see for example Astronomical Optics by Daniel Schroeder; classic articles on issues of spectrograph design include those by I.S. Bowen (1964, volume I of Stars and Stellar Systems) and R.G. Bingham (1979, QJRAS, 20, 395).
The reason for writing this is, in part, that observers have become more disconnected from the instrumentation as it becomes more complex. On my first observing run, I used an instrument that my advisor built, which the two of us could pick up, and take off the side panels to look at the optical path and adjust the internal focus. Today, there are still some hands-on opportunities, but nobody is going to let a green grad student put his or her hands inside a 8-meter class instrument. So the chance to see how things work is increasingly restricted to instrument builders and optical designers. For them, this is basic lore that ``everybody knows,'' but it rarely gets taught in a basic optics class.