A concave lens is kept in contact with a convex lens of focal length 20 cm.The combbination works as a convex lens of focal length 50 cm.Find the power of the concave lens.

Explanation

`f_(1)=` Focal length of concave lens,
`f_(2)=+20cm=` Focal length of convex lens
`f=` focal length of the combination of lenses
and `f=+50cm`
[`:.` Combination behaves convex lens]
We know `1/f=1/(f_(1))+1/(f_(2))`
`1/50=1/(f_(1))+1/20`
`1/(f_(1))=1/50-1/20`
`1/(f_(1))=(2-5)/100=-3/100`
`f_(1)=-100/3cm=-1/3m`
Power of concave lens `=P=1/(f_(1)("in m"))=1/(-1//3)`
`P=-3D`