Physics - Unit & Dimension Question with Solution | TestHub

Given, equation is$\frac{2}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}$....(i)

Differentiating the given equation, we have

$-\frac{2}{{\mathrm{f}}^2}\mathrm{ }\mathrm{df}=-\frac{1}{{\mathrm{v}}^2}\mathrm{dv}-\left(-\frac{1}{{\mathrm{u}}^2}\right)\mathrm{ }\mathrm{du}$

$=-\mathrm{p}\mathrm{ }\left(\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}\right)\mathrm{ }\left(\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}\right) \left(\because \mathrm{dv}=\mathrm{du}=\mathrm{p}\right)$

$=\frac{-2\mathrm{p}}{\mathrm{f}}\left(\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}\right)$[using Eq. (i)]

$\therefore \frac{\mathrm{df}}{\mathrm{f}}=\mathrm{p}\mathrm{ }\left(\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{v}}\right)$