Calculate the focal length of a convex lens which produces a virtual image at a distance of 50 cm of an object placed 20 cm in front of it.

Focal length is defined as the distance between the center of the lens and the curved part of the lens along with the focus.
Now,
Image distance, v = -50 cm.

Object distance u = -20 cm. 

Since the image is virtual it will be formed on the same side of the object.
From the lens formula,
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}$

$\frac{1}{\mathrm{f}}=\frac{1}{-50}-\frac{1}{-20}$

$\begin{array}{rcl}\frac{1}{\mathrm{f}}& =& -\frac{1}{50}+\frac{1}{20}\\ \frac{1}{\mathrm{f}}& =& \frac{-2+5}{100}\end{array}$

$=\frac{3}{100}$

 $\mathrm{f}=\frac{100}{3}\mathrm{cm}$