While the first telescopes to be used by astronomers used lenses in a long tube, most significant telescopes nowadays are reflecting telescopes. This means they have a large parabolic mirror that collects light from much of the sky and reflects it all to the focal point of the parabola, where there's some sort of light-collecting device that constructs the final image.
The problem with these mirrors is that they're very expensive to make. The resolution of the image is directly related to the smoothness and paraboloid-ness of the mirror, so it's crucial to polish the shape down just right. In most cases, I believe that the base shape is made of glass. It is cut, smoothed, and polished to near perfection, then coated with a thin layer of a reflective material like aluminum. The problem with this is that obtaining a good sample of glass and the process of polishing it takes time and costs a substantial amount. The cost of the mirror is often comparable to the cost of the rest of the telescope!
One possible alternative to the standard mirrored telescopes is the liquid mirror telescope. The premise is that a spinning cylinder of liquid naturally forms a paraboloid surface. By coating this liquid with a thin layer (about a millimeter thick) of mercury, which is both reflective and a liquid of the right viscosity, it is possible to obtain a paraboloid reflective surface for a telescope. Such telescopes were first proposed and used in the early nineteenth century, but they fell into disfavor with improving technology for more conventional techniques. More recently, Ermanno Borra, an astrophysicist based in Canada, revisited the idea and continues to explore it.
The resolution offered by such telescopes is high, and costs are just 1-10% that of a normal telescope mirror. The biggest downside is that a liquid mirror telescope cannot easily be tilted to track a star, since the liquid would slosh out of the correct mirror shape. Thus liquid mirror telescopes are pointed directly upward and used for large sky surveys for which tracking of an individual star or cluster is irrelevant. They've also proven useful for atmospheric studies, and Professor Borra is exploring the use of more viscous materials in order to enable some degree of tilting without damaging the function of the telescope.
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