The reflective telescope consists a parabolic concave reflector (objective) and a convex lens (eyepiece). The parabolic reflector (mirror) of this telescope replaces the objective convex lens of the regular telescope. The parabolic concave reflector, like the convex lens, focuses the light's rays.
The reflective telescope was introduced by Newton in the second half of the seventieth century. Using the reflector one avoids a central problem of the objective lens. Rays with different colour are refracted differently by the convex lens, in a way it is impossible to focus all of them to the same point. This problem does not exist in reflectors, which act in the same way on light in different colours.
The reflector telescope has a few more advantages over the two lenses telescope, which are originated from the size of the reflector, which enables higher magnifying power. It is easier to make a big reflector than a big lens. In addition the reflector telescope enables the astronomer to detect invisible light, which is not detected by lenses. Most of the astronomical telescopes, like the Hubble space telescope, are based on a parabolic reflector.
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