An object of height 1 cm is placed in front of a concave lens of focal length 40cm . If the object distance is 60 cm , find the position and height of the image .

Explanation

Data : `f=-40cm `(concave lens), `u=-60 cm, h_(1)=1 cm , v=? ,h_(2)=?`
`(i) 1/f =1/v-1/u therefore 1/v=1/f+1/u`
`therefore 1/v=(1)/(-40cm)+(1)/(-60 cm) =-((1)/(40cm)+(1)/(60cm))`
`=-((3+2)/(120 cm))=-(5)/(120)cm`
`therefore v=-(120)/(5)cm =-25 cm`
The image is formed at 24 cm from the lens . It is on the same side as the object .
(ii) `(h_(2))/(h_(1))=(v)/(u) therefore h_(2)=v/u h_(1)`
`therefore h_(2)=((-24 cm)/(-60))xx1 cm =0.4xx 1 cm =0.4 cm`
The heigth of the image is 0.4 cm