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Astronomers prefer reflecting telescopes over refracting telecopes for several reasons. The first is size. It is easier to make a large reflecting telecope than a large refracting telescope. A larger telescope means more light can be gathered and fainter objects can beseen. Older telescopes tended to make mirrors and lenses out of glass. Glass is a non-crystalline substance: it flows and deforms over time. For a reflecting telescope that is less of a problem because one whole side of the mirror is supported while a lens is supported on a thin edge which is less strong. In a reflecting telescope only one side is optically active, the mirror, while with a refracting telecope both sides of the lens must remain perfect. A mirror can be resurfaced more easily than lenses can be reground. For many years the 200 " dia. Mount Palomar telescope was the world's largest because a larger mirror began to warp and bend under its own weight. (An attempted 240" dia. in the Soviet Union had many problems.) The largest refractor is the Yerkes telescope whose lens is only 40 " in dia. Today larger reflectors can be built out of smaller elements (e.g hexagonals) which can be carefully positioned using computers to act a large single mirror. The Keck observator has two 10 m dia. (390 ") telescopes using this new design.
Finally there is the problem of chromatic aberration. Glass has a different index of refraction for different wavelengths. A lens will focus images of an object a different positions depending upon the wavelength observed. An image made of multiple wavelengths will be blurred because there is no single focal point for all the wavelengths at the same time. This is not a problem with a mirror which focuses all wavelengths at the same point.
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