An astronimical telescope is to be designed to have a magnifying power of 50 in normal adjustment. If the length of the tube is 102 cm, find the powers of the objective and the eyepiece.

Explanation

Given, `M_(oo)=50`
`therefore (f_(o))/(f_(e))=50`…(i)
Further, `L_(oo)=102 cm`
`therefore f_(o)+f_(e)=102 cm`….(ii)
Solving Eqs. (i) and (ii) we have
`f_(o)=100 cm and f_(e)=2 cm`
`therefore` Power of object, `P_(o)=1/1.0=1/D`
and power of eye piece,`P_(e)=1/0.02=50D`