Physics - Geometrical Optics Question with Solution | TestHub

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,$\frac{1}{-uP}+\frac{1}{-u}=\frac{1}{-f}$

$\Rightarrow \frac{1}{u}\left(\frac{1}{P}+1\right)=\frac{1}{f}$

$\Rightarrow u=\left(\frac{P+1}{P}\right)f$