A lens placed at a distance of 20 cm from an object produces a virtual image `2//3` the size of the object.Find the position of image,kind of lens and its focal length.

Explanation

As a image formed by lens is virtual and smaller tha the object
`:.` Given lens is a concave lens
`u=-20cm`
`m=2/3`
`m=v/u`
`impliesv/u=2/3`
`v=24/3=(2(-20))/3`
`=-40/3=-13.3cm`
We know `1/v-1/u=1/f`
`1/f=1/(-40//3)-1/(-20)`
`=-3/40+1/20`
`1/f=(-3+2)/40=-1/40`
`f=-40cm`