In Rome's Revolution, the Maksutov-Cassegrain Reflector is mentioned several times. The first time it is mentioned in context of Silas Hiram's telescope on what had been called New Earth and now is referred to as Helome. Silas brought the telescope to Alpha Centauri aboard the Ark I and he used it to visualize Earth. He was the first person to notice that Alnilam had disappeared which caused a cascade of events leading up to the discovery of the Stareaters.
The second mention of this type of telescope is that it is built into the eyes of the Vuduri giving them telescopic vision when they want it. Their retinas have been modified become reflective, like a cat's retina, called a tapetum. There is a tiny reflective mirror in the front of their iris that serves as the focusing mirror which then sends the image onto the fovea.
The way a Maksutov-Cassegrain reflector works is that light comes through the transparent front lens, is focused on to the back mirror (or tapetum) which refocuses the light onto the prism and onto the eyepiece. The effect of all of this is that the focal length of the telescope is effectively three times that of a traditional telescope for the same length. It makes for a very compact, yet powerful, design.
From Wikipedia:
The Maksutov–Cassegrain is a variation of the Maksutov telescope named after the Soviet/Russian optician and astronomer Dmitri Dmitrievich Maksutov. It starts with an optically transparent corrector lens that is a section of a hollow sphere. It has a spherical primary mirror, and a spherical secondary that in this application is usually a mirrored section of the corrector lens.
Here is a small picture of the optical path (thank you Wikipedia):
