Question

Why must both the objective and the eyepiece of a compound microscope have short focal lengths?

Answer 1

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 |u_o| should be slightly more than f_o. But a microscope is used for nearby objects that are kept near the objective.

Hence, for these objects the value of |u_o| is less, hence the value of f_o 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 f_e is kept less.