Although some discoveries were made with these very long  instruments, this form of telescope had reached its limits. By  the beginning of the eighteenth century very long telescopes  were rarely mounted any more, and further increases of power  came, beginning in the 1730s, from a new form of telescope, the  reflecting telescope.



Since it was known that the telescopic effect could be achieved  using a variety of combinations of lenses and mirrors, a number  of scientists speculated on combinations involving mirrors. Much  of this speculation was fueled by the increasingly refined  theoretical study of the telescope. In his  Dioptrique, appended to his Discourse on  Method of 1637, Renè Descartes addressed the  problem of spherical aberration, already pointed out by  others. In a thin spherical lens, not all rays from  infinity--incident parallel to the optical axis--are united at  one point. Those farther from the optical axis come to a focus  closer to the back of the lens than those nearer the optical  axis. Descartes had either learned the sine law of refraction  from Willebrord Snell (Snell's Law) or had discovered it independently, and this allowed him to  quantify spherical aberration. In order to eliminate it, he  showed, lens curvature had to be either plano-hyperboloidal or  spherico-ellipsoidal. His  demonstration led many to attempt to make plano-hyperboloidal objectives, an effort which was doomed to failure by the state of the art of  lens-grinding. Others began considering the virtues of a concave  paraboloidal mirror as primary receptor: it had been known since  Antiquity that such a mirror would bring parallel incident rays  to a focus at one point.



A second theoretical development came in 1672, when Isaac Newton  published his celebrated paper on light and colors. Newton  showed that white light is a mixture of colored light of  different refrangibility: every color had its own degree of  refraction. The result was that any curved lens would decompose  white light into the colors of the spectrum, each of which comes  to a focus at a different point on the optical axis. This  effect, which became known as chromatic aberration, resulted in  a central image of, e.g., a planet, being surrounded by circles  of different colors. Newton had developed his theory of light several years before publishing his paper, when he had turned  his mind to the improvement of the telescope, and he had  despaired of ever ridding the objective of this defect. He  therefore decided to try a mirror, but unlike his predecessors  he was able to put his idea into practice. He cast a two-inch  mirror blank of speculum metal (basically copper with some tin)  and ground it into spherical curvature. He placed it in the  bottom of a tube and caught the reflected rays on a 45°  secondary mirror which reflected the image into a convex ocular  lens outside the tube. He sent this  little instrument to the Royal Society, where it caused a  sensation; it was the first working reflecting telescope. But  the effort ended there. Others were unable to grind mirrors of  regular curvature, and to add to the problem, the mirror  tarnished and had to be repolished every few months, with the  attending danger of damage to the curvature.



The reflecting telescope therefore remained a curiosity for  decades. In second and third decades of the eighteenth century,  however, the reflecting telescope became a reality in the hands  of first James Hadley and then others. By the middle of the  century, reflecting telescopes with primary mirrors up to six  inches in diameter had been made. It was found that for large  aperture ratios (the ratio of focal length of the primary to its  aperture, as the f-ratio in modern cameras for instance), f/10  or more, the difference between spherical and paraboloidal  mirrors was negligible in the performance of the telescope. In  the second half of the eighteenth century, in the hands of James  Short and then William Herschel, the reflecting telescope with  parabolically ground mirrors came into its own.



Source: http://cnx.org/content/m11932/latest/