Question

The minimum distance between an object and its real image formed by a thin convex lens of focal length $f$ is $Kf$. Find the value of $K$.

• A. $1$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is B $4$

Since object and image is real,
Let distsnce between them be $d$

Object distance $u=$ $-x$
Image distance $v$ = $d-x$

From Lens formula

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{d-x}-\frac{1}{-x}=\frac{1}{f}$
$\frac{1}{d-x}+\frac{1}{x}=\frac{1}{f}$
$df=(d-x)x$
$x^2-dx+df=0$

For a quadratic equation to have real roots determinant has to be $\ge 0$

$d^2-4df\ge 0$
$d^2\ge 4df$
$d\ge 4f$

$\therefore K=4$