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

#### Solution

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.