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  4. A concave lens of focal length f produces an image (1 / x) of the size of the object. The distance of the object from the lens is

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Q. A concave lens of focal length $f$ produces an image $(1 / x)$ of the size of the object. The distance of the object from the lens is

Ray Optics and Optical Instruments

Solution:

$m=\frac{f}{f+u}$
For virtual image $m=+\frac{1}{x}$
$+\frac{1}{x}=\frac{-f}{-f+u}$
$u=-f(x-1)$