question_answer

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

Correct Answer: A

Solution :

                   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 \[\frac{1}{f}=\frac{1}{+y}-\frac{1}{-(24-x)}\]\[\Rightarrow \]\[\frac{1}{y}=\frac{1}{f}-\frac{1}{(24-x)}\]     .....(ii) From equation (i) and (ii) \[\frac{1}{x}-\frac{1}{f}=\frac{1}{f}-\frac{1}{(24-x)}\]\[\Rightarrow \]\[\frac{1}{x}+\frac{1}{(24-x)}=\frac{2}{f}=\frac{2}{9}\] \[\Rightarrow \]\[{{x}^{2}}-24x+108=0\]. After solving the equation \[x=18\ cm\], 6 cm.