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Q. A concave 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:

$m=\frac{m}{f+u}$
$-2=\frac{\frac{1}{3}}{\frac{1}{3}+u}$
$-\frac{2}{3}-2 u=\frac{1}{3}$
or $-2 u=\frac{1}{3}+\frac{2}{3}=1$ or $u=-\frac{1}{2} m =-0.5 m$