An object `25` cm high is placed in front of a convex lens of focal length `30` cm . If the height of image formed is `50` cm , find the distance between the object and the image (real and virtual)?

Explanation

As object is in front of the lens , it is real and as

`h_(1) = 25 cm f= 30 cm h_(2) = - 50 cm`
`m = (h_(2))/( h_(1)) = (-50)/( 25) = 2`
`m = ( f)/( f+ u) rArr -2 = (30)/( 30+ u)`
`u= - 45 cm rArr m = (v )/(u ) rArr -2 = ( v)/( -45)`
`rArr v= 90 cm `
As in this situation object and image are on opposite sides of lens the distance between object and image `d_(1) = u + v= 45 + 90 = 135 cm`