The distance between two point sources of light is 24 cm. Where should be a converging lens of focal length 9 cm must be placed, so that the images of both the point sources are formed at the same point?
A
6 cmor18 cm either of the sources
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B
9 cm from either of the sources
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C
8 cmor18 cm from either of the sources
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D
5 cm from either of the sources
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Solution
The correct option is A6 cmor18 cm either of the sources
Let the lens is placed at a distance x from the s1 and image of the point source s1 is formed at v1.
For source s1, applying the lens formula u=−x f=+9 ⇒1v1−1−x=19
or 1v1=19−1x......(i)
For source s2, object distance u=−(24−x) ⇒1v2−1−(24−x)=19
or 1v2=19−1(24−x)....(ii)
The sign of image distance for s1 and s2 will be opposite. ⇒v1=−v2
or 1v1=−1v2 ⇒19−1x=−19+1(24−x)
or , 29=x+24−xx(24−x)
or, −2x2+48x−216=0
or, x2−24x+108=0
or, x2−18x−6x+108=0 x(x−18)−6(x−18)=0 ∴x=6 cmor18 cm
Why this question?Tip: From the principle of reversibility of light ifposition of both sources are interchanged then it won't affect the final image formation.