Physics - Geometrical Optics Question with Solution | TestHub

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. $$\begin{array}{rl}& \therefore \frac{1}{\mathrm{v}}-\frac{1}{-\mathrm{u}}=\frac{1}{\mathrm{F}}\\ & \therefore \frac{1}{\mathrm{v}}=\frac{1}{\mathrm{F}}-\frac{1}{\mathrm{u}}\end{array}$$ Multiplying by $\mathrm{v}$, $$\begin{array}{rl}1& =\frac{\mathrm{v}}{\mathrm{F}}-\frac{\mathrm{v}}{\mathrm{u}}\\ \therefore 1& =\frac{\mathrm{v}}{\mathrm{F}}-\mathrm{m}\dots \left(\because \frac{\mathrm{v}}{\mathrm{u}}=\mathrm{m}\right)\\ \therefore \frac{\mathrm{v}}{\mathrm{F}}& =1+\mathrm{m}\\ \therefore \mathrm{v}& =\mathrm{F}(1+\mathrm{m})\end{array}$$