d
(d) From mirror formula \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\) .....\((i)\)

Differentiating equation \((i),\) we obtain

\(0 = - \frac{1}{{{v^2}}}dv - \frac{1}{{{u^2}}}du\) \( \Rightarrow dv = - {\left({\frac{v}{u}} \right)^2}du\) .....\((ii)\)

Also from equation \((i)\) \(\frac{v}{u} = \frac{f}{{u - f}}\) .....\((iii)\)

From equation \((ii)\) and \((iii)\) we get \(dv = - {\left({\frac{f}{{u - f}}} \right)^2}.\;l\)

Therefore size of image is \({\left({\frac{f}{{u - f}}} \right)^2}l.\)