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  • Two point light sources are 24cm apart. At what distance from one source, a convex lens of focal length 9cm be kept in between them, so that the images of both the sources are formed at the same pl

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

Option: 1

6cm


Option: 2

9cm


Option: 3

12cm


Option: 4

15cm


Answers (1)

best_answer

The given condition will be satisfied only if one source \left(\mathrm{S}_1\right)  placed on one side such that u<f (i.e. it lies under the focus). The other source \left(\mathrm{S}_2\right)  is placed on the other side of the lens such that u>f (i.e. it lies beyond the focus).
If \left(\mathrm{S}_1\right) is the object for lens then

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

If \mathrm{S_2} is the object for lens then

\mathrm{\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)

\mathrm{\frac{1}{x}-\frac{1}{f}=\frac{1}{f}-\frac{1}{(24-x)}}


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

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

On solving we have  \mathrm{ x=18 \mathrm{~cm}, 6 \mathrm{~cm} }.

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Gunjita

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