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.

Object distance, $u$ = $-$20 cm     (negative sign shows that the object is placed on the left side of the lens)

Image distance, $v$ = $-$50 cm     (negative sign shows that the image is virtual)

To find: Focal length $(f)$ of the convex lens.

Solution:

According to the lens formula, we know that:

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

Substituting the given values in the formula we get-

$\frac {1}{(-50)}-\frac {1}{(-20)}=\frac {1}{f}$

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

$\frac {1}{f}=\frac {-2+5}{100}$

$\frac {1}{f}=\frac {3}{100}$

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

$f=+33.3$

Thus, the focal length $f$ of the convex lens is 33.3 cm.