Two convex lenses of focal lengths 2 cm and 6 cm, respectively are arranged to form a microscope. A small object is placed at 2.2 cm from the objective. If the image appears to be 20 cm from the eyepiece, what is the distance between objective and eyepiece?

Explanation

Consider objective be `L_(1)`,
`u=-2.2cmandf_(1)=+2cm`

`therefore 1/v+1/2.2=1/2" "(because1/v-1/u=1/f)`
`rArr1/v=1/2-1/2.2=(2.2-2)/4.4=0.2/4.4=1/22`
`thereforev=+22cm`
So, `L_(1)A_(1)=22cm`
Consider eyepiece be `L_(2)`,
`v=-20cm,f_(2)=+6cm`
`therefore-1/20-1/u=1/6`
`rArr-1/u=1/6+1/20=(20+60)/120=26/120`
`thereforeu=(-120)/26=(-60)/13`
So, `A_(1)L_(2)=60/13=4.61cm`
Distance between objective and eyepiece
`L_(1)L_(2)=L_(1)A_(1)+A_(2)L_(1)`
= `22+4.61=26.61` cm