In a convex lens of focal length F , the minimum distance between...

Let $L$ is the distance between a real object and its real image formed by a convex lens, then as $L=(|u|+|v|) =(\sqrt{u}-\sqrt{v})^2+2 \sqrt{u v}$ L will be minimum, when $(\sqrt{u}-\sqrt{v})^2=0 \text{ i.e., } u=v$ Putting, $u=-u$ and $v=+u$ in lens formula, $\frac{(0}{v}-\frac{@}{u}=\frac{\text{ @) }}{F} \frac{(0}{u}-\frac{®}{-u}=\frac{\text{ ๑) }}{F} u=2 F \therefore \quad(L)_{\min }=2 \sqrt{2-\times 2}=4 (U \operatorname{sing}(\mathrm{i}))$