The size of the real image produced by a convex lens of focal length \(\mathrm{F}\) is ' \(\mathrm{m}\) ' times the size of the object. The image distance from the lens is

From lens formula, \(\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{~F}}\)
For a convex lens, \(\mathrm{u}\) is negative, \(\mathrm{v}\) and \(\mathrm{F}\) are positive.
\(
\begin{aligned}
& \therefore \quad \frac{1}{\mathrm{v}}-\frac{1}{-\mathrm{u}}=\frac{1}{\mathrm{~F}} \\
& \therefore \quad \frac{1}{\mathrm{v}}=\frac{1}{\mathrm{~F}}-\frac{1}{\mathrm{u}}
\end{aligned}
\)
Multiplying by \(\mathrm{v}\),
\(
\begin{aligned}
1 & =\frac{\mathrm{v}}{\mathrm{F}}-\frac{\mathrm{v}}{\mathrm{u}} \\
\therefore \quad 1 & =\frac{\mathrm{v}}{\mathrm{F}}-\mathrm{m} \quad \ldots\left(\because \frac{\mathrm{v}}{\mathrm{u}}=\mathrm{m}\right) \\
\therefore \quad \frac{\mathrm{v}}{\mathrm{F}} & =1+\mathrm{m} \\
\therefore \quad \mathrm{v} & =\mathrm{F}(1+\mathrm{m})
\end{aligned}
\)