Two point surces `S_(1) and S_(2)` are 24 cm apart. Where should a convex lens of focal length 9 cm be placed them , so that the images of both sources are formed at the same place ?

Options

A. 8 cm
B. 12 cm
C. 6 cm
D. 10cm

Answer

B

Explanation

The given condition will be satisfied only if one source `(S_(1))` placed on one side such that ` u lt f` (i.e. it lies under the focus . The other source `(S_(2))` is placed on the other side of the lens such that `u gt f` (i.e. it lies beyond the forcus )
If `S_(1)` is the object for the lens, then
`(1)/(f) = (1)/(-y) -(1)/(-x)`
`rArr (1)/(y) = (1)/(x) -(1)/(-f) " ". . . (i)`
If `S_(2)` is the object for the lens, then
`(1)/(f) =(1)/(+y) -(1)/(-(24 - x))`
`rArr (1)/(-y) = (1)/(f) - (1)/((24 -x))" ". . . (ii)`
From the Eqs. (i0 and (ii), we get
`(1)(x) - (1)/(f) = (1)/(f) -(1)/((24 - x))`
`(1)/(x) +(1)/((24 - x)) = (2)/(f) = (2)/(7)`
`x^(2) - 24 + 108 = 0`
`x = 18 ` cm and x = 6 cm
So, the correct answer will be 6 cm .