A concave lens is placed in contact with a convvex lens of focal lenght 25 cm.the combinatin produces a real image at a distance of 80 cm,when the object is at a distance of 40 cm.What is the focal length of the concave lens?

Explanation

`f_(1)=` Focal length of concave lens
`f_(2)=25cm=` Focal length of convex lens
Let `f=` focal of combination of lenses
`v=+80cm`
`u=-40cm`
By lens formula we have
`1/v-1/u=1/f`
`1/v-1/u=1/(f_(1))+1/(f_(2))`
`1/80-1/(-40)=1/(f_(1))+1/25`
`1/(f_(1))=1/80+1/40-1/25=(5+10-6)/400`
`1/(f_(1))=-400cm`