A concave lens is placed in contact with a convex lens of focal length `25 cm`. The combination produces a real image at a distance of `80 cm`, when an object is at a distance of `40 cm`. What is the focal length of concave lens ?

Explanation

Here, `f_(1) = 25cm, f_(2) = ?`
For the combination of focal length `F`,
`u = - 40 cm, v = +80 cm`.
As `(1)/(F) = (1)/(v) - (1)/(u)`
`:. (1)/(F) = (1)/(80) - (1)/(-40) = (1 + 2)/(80) = (3)/(80)`
As `(1)/(f_(1)) + (1)/(f_(2)) = (1)/(F)`
`:. (1)/(f_(2)) = (1)/(F) - (1)/(f_(1)) = (1)/(80) - (1)/(25) = (15 - 16)/(400)`
`(1)/(f_(2)) = -(1)/(400), :. f_(2) = - 400 cm`