Answer the following question:

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

A compound microscope produces an angular magnification of [(25/f_e) + 1]

where,

f_e = focal length of the eyepiece

It can be inferred that if f_e is small, then angular magnification of the eyepiece will be large.

The angular magnification of the objective lens of a compound microscope is given as

1/(|u₀|f₀)

Where, u_o = object distance for the objective lens

f_o = focal length of the objective

The magnification is large when u_o > f_o. In the case of a microscope, the object is kept close to the objective lens. Hence, the object distance is very little. Since, u_o is small, f_o will be even smaller. Therefore, f_e and f_o are both small in the given condition.