Physics - Geometrical Optics Question with Solution | TestHub

For a concave mirror, the focal length is taken as $-f$ and the object distance as $-u$ (where $f$ and $u$ are positive distances).

Since the image is real, it is inverted, so the magnification $m$ is negative. Thus, $m=-n$.

The magnification formula in terms of focal length and object distance is given by:

$m=\frac{f}{f-u}$

Applying the sign convention:

$-n=\frac{-f}{-f-(-u)}$

$-n=\frac{-f}{-f+u}$

$-n(-f+u)=-f$

$nf-nu=-f$

$nu=nf+f$

$nu=(n+1)f$

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

The distance of the object from the mirror is $\left(\frac{n+1}{n}\right)f$.

Answer: $\left(\frac{\mathrm{n}+1}{\mathrm{n}}\right)\mathrm{f}$