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What is the magnifying power of a telescope that has a mirror with 250cm radius?
Reflecting telescope makes use of a concave mirror in place of the objective lens to bring a distant object onto focus. What is the magnifying power of a telescope that has a mirror with 250cm radius and an eye piece, whose focal length is 5.0cm?
For a concave mirror, the focal length is half the radius of curvature, so for your example, fl = 250 cm / 2 = 125 cm. The magnification of a mirror/lens optical system is objective fl / eyepiece fl, so for your system, this is 125 cm / 5 cm = 25 power.
One note: If your telescope uses a spherical mirror, it will show significant aberrations in the image unless the mirror diameter is < 1/10 of the focal length, so you would need a mirror < 12.5 cm in diameter, or a parabolic shape, or a correcting lens to bring the light from all parts of the mirror to focus at the same point.
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