Question: How does a telescope perform its task of viewing far-away objects?
About the article "Telescope", section "Abstract".

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A tower viewer is a telescope or binoculars permanently mounted on a stalk.
The device magnifies objects seen through its lenses, allowing users to see farther and more clearly than they could with the naked eye or with less powerful viewing devices.
Tower viewers are typically metallic and most swivel horizontally and vertically (within given axes of rotation) to permit a range of view.
The viewing machines are commonly placed in tourist destinations and scenic lookouts for the purpose of viewing attractions and events of interest; they are also used in residential, business, recreational and government locations for the purposes of surveillance and safety monitoring.
Tower viewers are known by a variety of names, which include:  coin(-operated) binoculars, coin(-operated) telescope, coin(-operated) scope, coin(-operated) viewer  donation viewer  free use viewer  observation binoculars, observation telescope, observation viewer  optical ranger, optical sight  outdoor viewer  non-coin(-operated) binoculars, non-coin(-operated) telescope, non-coin(-operated) scope, non-coin(-operated) viewer  Pinnacle Scope  revenue binoculars, revenue telescope  scenic magnifier, scenic telescope, scenic viewer  spyglass viewer, spyglasses  stationary binoculars, stationary telescope  tower binoculars, tower scope, tower telescope  view master, viewfinder, viewer, viewing scope, viewing machine, viewing stand, viewing telescope  
The Carter Observatory houses two main telescopes within its main building and a third telescope nearby.
The Thomas Cooke telescope, a historic 9-inch Cooke Refractor named after Thomas Cooke, serves primarily for public observing sessions.
The Ruth Crisp telescope, described below, arrived as a donation in the 1960s.
Not far from its main building, the Carter Observatory operates the Thomas King Observatory, used until recently for public viewing of the sun. 
Conception, design and aims.
Proposals and precursors.
In 1923, Hermann Oberth—considered a father of modern rocketry, along with Robert H. Goddard and Konstantin Tsiolkovsky—published "" ("The Rocket into Planetary Space"), which mentioned how a telescope could be propelled into Earth orbit by a rocket.
The history of the Hubble Space Telescope can be traced back as far as 1946, to the astronomer Lyman Spitzer's paper "Astronomical advantages of an extraterrestrial observatory".
In it, he discussed the two main advantages that a space-based observatory would have over ground-based telescopes.
First, the angular resolution (the smallest separation at which objects can be clearly distinguished) would be limited only by diffraction, rather than by the turbulence in the atmosphere, which causes stars to twinkle, known to astronomers as seeing.
At that time ground-based telescopes were limited to resolutions of 0.5–1.0 arcseconds, compared to a theoretical diffraction-limited resolution of about 0.05 arcsec for a telescope with a mirror 2.5 m in diameter.
Second, a space-based telescope could observe infrared and ultraviolet light, which are strongly absorbed by the atmosphere.
Spitzer devoted much of his career to pushing for the development of a space telescope.
In 1962, a report by the US National Academy of Sciences recommended the development of a space telescope as part of the space program, and in 1965 Spitzer was appointed as head of a committee given the task of defining scientific objectives for a large space telescope.
Space-based astronomy had begun on a very small scale following World War II, as scientists made use of developments that had taken place in rocket technology.
The first ultraviolet spectrum of the Sun was obtained in 1946, and the National Aeronautics and Space Administration (NASA) launched the Orbiting Solar Observatory (OSO) to obtain UV, X-ray, and gamma-ray spectra in 1962.
An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel space program, and in 1966 NASA launched the first Orbiting Astronomical Observatory (OAO) mission.
OAO-1's battery failed after three days, terminating the mission.
It was followed by OAO-2, which carried out ultraviolet observations of stars and galaxies from its launch in 1968 until 1972, well beyond its original planned lifetime of one year.
The OSO and OAO missions demonstrated the important role space-based observations could play in astronomy, and in 1968, NASA developed firm plans for a space-based reflecting telescope with a mirror 3 m in diameter, known provisionally as the Large Orbiting Telescope or Large Space Telescope (LST), with a launch slated for 1979.
These plans emphasized the need for manned maintenance missions to the telescope to ensure such a costly program had a lengthy working life, and the concurrent development of plans for the reusable space shuttle indicated that the technology to allow this was soon to become available. 
The exact shape of this region varies depending on what kind of camera lens is being simulated, but typically it is a frustum of a rectangular pyramid (hence the name).
The planes that cut the frustum perpendicular to the viewing direction are called the "near plane" and the "far plane".
Objects closer to the camera than the near plane or beyond the far plane are not drawn.
Sometimes, the far plane is placed infinitely far away from the camera so all objects within the frustum are drawn regardless of their distance from the camera.
Viewing frustum culling or view frustum culling is the process of removing objects that lie completely outside the viewing frustum from the rendering process.
Rendering these objects would be a waste of time since they are not directly visible.
To make culling fast, it is usually done using bounding volumes surrounding the objects rather than the objects themselves. 
This term describes what can be seen using a telescope, when viewing an object or range the observer may use many different techniques.
Understanding what can be viewed and how to view it depends on the field of view.
Viewing an object at a size that fits entirely in the field of view is measured using the two telescope properties—focal length and aperture, with the inclusion of an ocular eyepiece with suitable focal length (or diameter).
Comparing the observable world and the angular diameter of an object shows how much of the object we see.
However, the relationship with the optical system may not result in high surface brightness.
Celestial objects are often dim because of their vast distance, and detail may be limited by diffraction or unsuitable optical properties.