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  4. A convex lens of focal length (1/3) m forms a real inverted image twice in size of the object. The distance of the object from the lens is

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Q. A convex lens of focal length $\frac{1}{3}\, m$ forms a real inverted image twice in size of the object. The distance of the object from the lens is

Ray Optics and Optical Instruments

Solution:

For lens,
$m=-2, f=+\frac{1}{3} m \Rightarrow \frac{v}{u}=-2$ or $v=-2 u$
As $\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{-2 u}-\frac{1}{u}=3$
$\frac{-3}{2 u}=3 \Rightarrow u=\frac{-1}{2} m =-0.5\, m$