Question

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

Answer 1

The angular magnification produced by the eyepiece of a compound microscope is `[(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/((|"u"_"o"|"f"_"o"))`

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.