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
$L = \left(|u|+|v|\right)$
$\,=\left(\sqrt{u}-\sqrt{v} \right)^2+2\sqrt{uv}\quad\quad\quad\quad ...\left(i\right)$
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,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{F}$
$\frac{1}{u}-\frac{1}{-u}=\frac{1}{F}$
$u = 2F$
$\therefore \, \left(L\right)_{min}= 2\sqrt{2F\times2F}=4F \quad\left(Using \left(i\right)\right)$