Question

The minimum distance between an object and its real image formed by a convex lens is :

• A. $\frac{2}{3}f$
• B. $2f$
• C. $\frac{5}{2}f$
• D. $4f$

Answer 1

The correct option is D $4f$

Let the between object and real image be $d$.

Let the distance of object from the lens is $x$

So the distance of image and lens be $d-x$

Using the lens equation :

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f}=\frac{1}{d-x}-\frac{1}{-d}$

$x=\frac{d\pm \sqrt{d^2-4fd}}{2}$ ...(1)

So for real $x$

$\sqrt{d^2-4fd}\ge 0$

So $d\ge 4f$

So minimum distance between object and image is 4f.