A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses. Although large refracting telescopes were very popular in the second half of the 19th century, for most research purposes the refracting telescope has been superseded by the reflecting telescope which allows larger apertures. A refractor's magnification is calculated by dividing the focal length of the objective lens by that of the eyepiece.
A reflecting telescope (also called a reflector) is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Reflecting telescopes come in many design variations and may employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a "catoptric" telescope.
Catadioptric telescopes are optical telescopes that combine specifically shaped mirrors and lenses to form an image. This is usually done so that the telescope can have an overall greater degree of error correction than their all lens or mirror counterparts with a consequently wider aberration-free field of view. Their designs can have simple all spherical surfaces and can take advantage of a folded optical path that reduces the mass of the telescope, making them easier to manufacture. Many types employ “correctors”, a lens or curved mirror in a combined image-forming optical system so that the reflective or refractive element can correct the aberrations produced by its counterpart.