What is the diameter of the image of Mars formed by a telescope mirror w/ focal length of 1.75m (see details)?
Saturday, December 4th, 2010 at
9:48 am
The diameter of Mars is 6794 km, and its minimum distance from the earth is 5.58x10^7 km. (NOTE: A telescope mirror is convex.)
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Assume that the planet is on the optical axis of the mirror. Rays from the extreme edges of the planet to the centre point of the mirror will form a triangle which is similar to that formed by the reflected rays which then pass on to the extreme edges of the image. So the ratio of the diameter of Mars to its distance from the telescope is the same as that of the diameter of the image (d) to the focal length of the mirror. we can write -
d/1.75 = 6794/5.58*10^7
d = 1.75*6794/5.58×10^7 = 213*10^-6m
Note – the mirrors of astronomical telescopes are concave.