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The distance between two point sources of light is 24 cm. Where should a convergent lens of focal length 9 cm be placed between them to obtain images of both sources at the same point ? |
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Answer» u = 6 or 18 cm  The lens has to be so adjusted that real IMAGE P.Q. of PQ COINCIDES with virtual image `P_(1).Q_(1). of P_(1) Q_(1)`. Let u be DISTANCE of lens from first source. For real image, `(1)/(v) - (1)/((-u)) = (1)/(9)` `(1)/(v) = (1)/(9) - (1)/(u)` For virtual image, `(1)/(-v)-(1)/(-(24-u))=(1)/(9)` `-(1)/(9) + (1)/(u) + (1)/(24-u) = (1)/(9)` `(2)/(9) = (1)/(24)-u + (1)/(u), therefore u^(2) - 24 u + 108 = 0` u = 6 or 18 cm |
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