A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at the least distance of distinct vision (25 cm)? What is the magnifying power of the microscope in?

Explanation

`f_(o)=2cm`
`f_(e )=6.25 cm`
Distance between objective lens and eye piece `=L=17cm`
Distance of the object from objective lens `=u_(o)=`?
Distance of final image from the eye-piece `=V_(e )= -25 cm`

We know `-(1)/(u_(e )) +(1)/(v_(e )) =(1)/(f_(e ))`
`-(1)/(u_(e ))+(1)/(-25)=(1)/(6.25)`
`-(1)/(u_(e ))=(1)/(6.25) +(1)/(25) =(25+6.25)/(25xx6.25)`
`v_(e )= -(25xx6.25)/(31.25)= -5cm`
We know `u_(o)+|v_(e )| =L`
`v_(o)+5=17`
`v_(o)=17-5=12cm`
Also `-(1)/(u_(o)) +(1)/(v_(o)) =(1)/(f_(o))`
`-(1)/(u_(o)) +(1)/(12)=(1)/(2)`
`-(1)/(u_(o)) =(1)/(2)-(1)/(12)=(6-1)/(12) =(5)/(12)`
`rArr u_(o) = -(12)/(5) = -2.4 cm`
So distance of the object from objective lens = 2.4 cm.