question_answer

Two point source \[{{S}_{1}}\] and \[{{S}_{2}}\] are 24 cm apart. Where a convex lens of focal length 9 cm should be placed in between them so that the images of both sources are formed at the same place?          

A) 6 cm from \[{{S}_{1}}\]

B) 15 cm from \[{{S}_{1}}\]

C) 10 cm from \[{{S}_{1}}\]

D) 12 cm from \[{{S}_{1}}\]

Correct Answer: A

Solution :

[a] In this case, one of the image will be real and the other virtual. Let us assume that image of \[{{S}_{1}}\] is real and that of \[{{S}_{2}}\] is virtual. Applying \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\] For \[{{S}_{1}}:\frac{1}{y}+\frac{1}{x}=\frac{1}{9}\]                          ?.(i) For \[{{S}_{2}}:\frac{1}{y}+\frac{1}{24-x}=\frac{1}{9}\]                                 ?(ii) Solving eqs. (i) and (ii), we get \[x=6cm\,\]