A telescope has an objective of focal length `50cm` and an eyepiece of focal length `5cm.` The least distance of distinct vision is `25cm.` The telescope is focused for distinct vision on a scale `2m` away from the objective. Calculate (a) magnification produced and (b) separation between objective and eyepiece.

Explanation

Given `f_(0)=50cm` and `f_(e)=5cm`
For objective
`1/v_(0) - 1/(-200)=1/50 :. V_(0)=200/3cm`
`m_(0)=v_(0)/u_(0)=((200//3))/(-200)=-1/3`
For eyepiece
`2/(-25) - 1/u_(e)=1/5`
`:.u_(e)=-25/6 cm` and `m_(e)=v_(e)/u_(e)=(-25)/(-(25//6))=6`
a)Magnification `m=m_(0)xxm_(e)=-2`
b) Seperation between objective and eyepiece
`L=v_(0+ |u_(e)|=200/3 + 25/6=425/6=70.83cm`