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

Explanation

`(1)/(v_(1))-(1)/(u)=(1)/(f_(1))" "rArr(1)/(v_(1))=(1)/(f_(1))+(1)/(u_(1))`
`=(1)/(20)+(1)/(-40)=(1-2-7)/(-40)=(1)/(40)`
`v_(1)=40 cm`
Here, image by `L_(3)` is formed at focus. So, the object should lie at infinity for `L_(3)`. Hence, `L_(2)` will produce image at infinity. So, we can conclude that object for `L_(2)` should be at its focus.
But, we have seen above that image by `L_(1)` is formed at 40 right of `L_(1)` which is at 20 cm left of `L_(2)` (focus of `L_(2)`).
So, `X_(1)=" distance between "L_(1) and L_(2)=(40+20)cm=60 cm.`
Again distance between `L_(2) and L_(3)` does not matter as the image by `L_(2)` is formed at infinity. So, `X_(2)` can take any value.