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  4. A concave mirror of focal length f produces an image P time the size of the object. If the image is real, then the distance of the object from the mirror is

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Q. A concave mirror of focal length $f$ produces an image $P$ time the size of the object. If the image is real, then the distance of the object from the mirror is

NTA AbhyasNTA Abhyas 2022

Solution:

Given, Magnification, $M=\frac{I}{O}=-\frac{v}{u}=-P$
Or $v=uP.$
Using mirror's formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Here, the image of the real object is also real, therefore, v.u.f, all are on the negative side.
Hence, $\frac{1}{- u P}+\frac{1}{- u}=\frac{1}{- f}$
$\Rightarrow \, \, \, \frac{1}{u}\left(\frac{1}{P} + 1\right)=\frac{1}{f}$
$\Rightarrow \, \, \, u=\left(\frac{P + 1}{P}\right)f$