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Q. If $I_{1}$ and $I_{2}$ be the size of the images respectively for the two positions of lens in the displacement method, then the size of the object is given by

ManipalManipal 2009Ray Optics and Optical Instruments

Solution:

$\frac{I_{1}}{O}=\frac{v}{u}$
$\Rightarrow \frac{I_{2}}{O} =\frac{u}{v}$
$\therefore O^{2} =I_{1} I_{2}$
$O=\sqrt{I_{1} \times I_{2}}$