A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of equal focal length . What is the focal length of the combination ?

Explanation

let `f_(1)` is focal length of convex (converging) lens and `f_(2)` is focal length of concave (diverging) lens. Then their equivalent focalength `F` would be
`(1)/(F)=(1)/(f_(1))-(1)/(f_(2))=(f_(2)-f_(1))/(f_(1)f_(2))[because(1)/(F)=(1)/(f_(1))+(1)/(f_(2))]`
`therefore F=(f_(1)f_(2))/(f_(2)-f_(1))`