Question

Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place

• A. 6 cm
• B. 9 cm
• C. 12 cm
• D. 15 cm

Answer 1

Answer: (A)

6 cm

Answer 2

The given condition will be satisfied only if one source (S₁) placed on one side such that u < f (i.e. it lies under the focus). The other source (S₂) is placed on the other side of the lens such that u > f (i.e. it lies beyond the focus).

If $S _ { 1 }$ is the object for lens then $\frac { 1 } { f } = \frac { 1 } { - y } - \frac { 1 } { - x }$

$\Rightarrow$ $\frac { 1 } { y } = \frac { 1 } { x } - \frac { 1 } { f }$ ........(i)

If $S _ { 2 }$is the object for lens then $\frac { 1 } { f } = \frac { 1 } { + y } - \frac { 1 } { - ( 24 - x ) }$

$\frac { 1 } { y } = \frac { 1 } { f } - \frac { 1 } { ( 24 - x ) }$ ........(ii)

From equation (i) and (ii)

$\frac { 1 } { x } - \frac { 1 } { f } = \frac { 1 } { f } - \frac { 1 } { ( 24 - x ) }$ $\Rightarrow$ $\frac { 1 } { x } + \frac { 1 } { ( 24 - x ) } = \frac { 2 } { f } = \frac { 2 } { 9 }$

$\Rightarrow$ $x ^ { 2 } - 24 x + 108 = 0$

On solving the equation $x = 18 \mathrm {~cm}$ , 6 cm