What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

Explanation

Focal length of convex lens `=f_(1)+30cm`
focal length of concave lens `=f_(2)=-20cm`
Let focal length of the combinationof lenses `=f=?`
We know `1/f=1/(f_(1))+1/(f_(2))`
`1/f=1/30+1/(-20)=1/30-1/20`
`1/f=(2-3)/60=(-1)/60`
`f=60cm`
-ve sign shows that combination behaves as a diverging lens.