Question

In a convex lens of focal length $F$, the minimum distance between an object and its real image must be

• A. 3F
• B. 4F
• C. $\frac{3}{2}$
• D. 2F

Answer 1

Answer: (B)

Let L is the distance between a real object and its real image formed by a convex lens, then as
$L=\left(|u|+|v|\right)$
$={\left(\sqrt{u}-\sqrt{v}\right)}^2+2\sqrt{uv}...\left(i\right)$
L will be minimum, when
${\left(\sqrt{u}-\sqrt{v}\right)}^2=0$
$i.e.,u=v$
Putting, $u=-u$ and $v=+u$ in lensformula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{F}$
$\frac{1}{u}-\frac{1}{-u}=\frac{1}{F}$
$u=2F$
$\therefore {\left(L\right)}_{min}=2\sqrt{2F\times 2F}=4F\left(Using\left(i\right)\right)$