Your are given three lenses `L_(1), L_(2)` and `L_(3)` each of focal length 20cm. An object is kept at 40cm in front of `L_(1)` as shown. The final real image is formed at the focus I of `L_(3)`. Find the separation between `L_(1)` and `L_(2)` and `L_(3)`.

Explanation

For lens `L_(1)`
`(1)/(f_(1)) = ( 1)/( v_(1)) - ( 1)/( u_(1))`
`(1)/( 20) = ( 1)/( v_(1)) - (1)/( -40) rArr v_(1) = 40cm`
For lens `L_(3)` `(1)/( f_(3)) = ( 1)/( v_(3)) - ( 1)/( u _(3))`
`u_(3) = ? , f_(3) = + 20 cm, v_(3) = 20cm`
`(1)/( 20) = ( 1)/( 20) + ( 1)/( u_(3))`
`u_(3) = oo`
It shows that `L_(2)` must render the rays parallel to the common axis. It means that the image `(I_(1))`, formed by `L_(1)`, must be at a distance of 20cm from `L_(2)` ( at the focus of `L_(2)` )
Therefore, distance between `L_(1)` and `L_(2) = ( = 40 + 20) = 60 cm` and distance between `L_(2)` and `L_(3)` can have any value .