A converging beam of light forms a sharp image on a screen. A lens is placed in the path of the beam, at 10cm from the screen. It is found that the screen has to be moved 8 cm further away from the lens to obtain a sharp image. Find the focal length and nature of lens.

Explanation

As shown in figure, in this problem, object Ois virtual while image I real,
so that u = 10 cm and v=(10+8)= 18 cm and hence from lens formula, `(1)/(v) -(1)/(u ) =(1)/(f) `
we have `(1)/(18) -(1)/(10) =(1)/(f)`
which on simplification gives `f= -(90)/(4) 22.5cm `
i.e., the lens is diverging (concave) of focal length 22.5 cm