Question

The distance between two point sources of light is 24 cm and a converging lens is kept in between two sources. The object distances of two sources from a converging lens of focal length of 9 cm, so that the image distances of two sources are equal

• A. 12 cm
• B. 24 cm or 18cm
• C. 18 cm or 6 cm
• D. 24 cm

Answer 1

The correct option is C 18 cm or 6 cm

Here $u_1+u_2=-24$.......(1).

$\frac{1}{v_1}-\frac{1}{u_1}=\frac{1}{9}$

and for the virtual image

$\frac{1}{-v_1}-\frac{1}{u_2}=\frac{1}{9}$

$-(\frac{1}{u_1}+\frac{1}{u_2})=\frac{2}{9}⟹u_1{u}_2=108$.........(2)

On solving (1) and (2)

We get $u^2+24u+108=0⟹u=-18,-6$