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Question
Why must both the objective and the eyepiece of a compound microscope have short focal lengths?
Solution
The objective of the magnification of a microscope is `v_o/|u_o| = 1/((|u_o|/f_o - 1))`. It is clear from this that to increase this magnification, the value of |uo| should be slightly more than fo. But a microscope is used for nearby objects that are kept near the objective.
Hence, for these objects the value of |uo| is less, hence the value of fo has to be kept even less.
The magnification of the eyepiece is `(1 + "D"/"f"_"e")`; hence, it is clear that to increase it, the value of fe is kept less.
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