The distance between two point sources of light is `24cm.` Find out where would you place a converging lens of focal length `9cm,` so that the images of both the sources are formed at the same point.

Explanation

Using the relation,`1/v=1/u=1/f`
For `S_(1),1/v_(1)-1/(-x)=1/9rArrtherefore1/v_(1)=1/9-1/x….(i)`
For `S_(2)1/v_(2)-1/(-(24-x))=1/9`
`therefore1/v_(2)=1/9-1/(24-x)…(ii)`
Since, sign convention for `S_(1) and S_(2)` is just opposite. Hence,
`v_(1)=-v_(2)or 1/v_(1)=-1/v_(2)`
`therefore1/9-1/x=1/(24-x)-1/9`
Solving this equation we get, x=6 cm. Therefore the lens should be kept at a distance of 6 cm from either of the object.