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In compound microscope, we take such an objective lens which has small focal length. While in astronomical telescope, we take such an objective lens which has large focal length.

Why don't we use same objective lens in both? The function of both the devices is to enlarge an object at infinity.

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    $\begingroup$ What do you mean by "enlarge an object infinity?" Do you mean enlarge an object at infinity, or enlarge an object infinitely (i.e., maximize magnification)? $\endgroup$ – Ben Crowell Aug 14 '13 at 13:46
  • $\begingroup$ eddited......:) $\endgroup$ – Rafique Aug 14 '13 at 13:56
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    $\begingroup$ OK, thanks for the clarification. As explained in Kyle Kanos's answer, the microscope doesn't work on objects at infinity. $\endgroup$ – Ben Crowell Aug 14 '13 at 15:11
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Wikipedia's article on Focal length explains pretty clearly (emphasis mine):

In most photography and all telescopy, where the subject is essentially infinitely far away, longer focal length (lower optical power) leads to higher magnification and a narrower angle of view; conversely, shorter focal length or higher optical power is associated with a wider angle of view. On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length (higher optical power) leads to higher magnification because the subject can be brought closer to the center of projection.

So it basically depends on the fact that most of our astronomical sources are at distances larger than $\sim10^{18}$ cm away from us, while our microscopic objects are less than $\sim100$ cm away from us.

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