Question

Where should a convex lens of focal lensth 9cm be placed (in cm) between two point sources `S_(1)` and `S_(2)` where are 24 cm apart, so that images of both the sources are formed at the same place. You have to find distance of lens from `S_(1)` or `S_(2)` whichever is lesser.

Answer 1

Correct Answer - 6
Let both the images are formed at I. For `S_(1)` , the image is virtual and for `S_(2)` , the image is real.
For `S_(1): (1)/(v)-(1)/(u)=(1)/(f)rArr (1)/(-y)-(1)/(-x)=(1)/(9)` (i)
For `S_(2): (1)/(y)-(1)/(-(24-x))=(1)/(9)` (ii)
Form (i) and (ii) `(1)/(x)+(1)/(24-x)=(1)/(9)`
`rArr x^(2)-24x+108=0`
`rArrx=6cm` and 18cm
But `x lt f`. So answer is 6cm