A converging beam of light forms a sharp image on a screen. A lens is placed in the path of the beam at `10 cm` 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 the lens.

Answer

`22.5 cm`, concave

Explanation

Here, `u = + 10 cm`
`v = + (10 + 8) = 18 cm`,

`(1)/(f) = (1)/(v) - (1)/(u) = (1)/(18) - (1)/(10) = -(8)/(180)`
`f = - (180)/(8) = - 22.5 cm`
As `f` is negative, the lens must be concave.