A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.

Object distance, $u$ = $-$15 cm     (negative sign shows that the object is placed on the left side of the lens)

Magnification, $m$ = $-$3              (negative sign implies that the image is inverted)

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

Solution:

According to the magnification formula, we know that:

$m=\frac {v}{u}$

Substituting the given values in the formula we get-

$-3=\frac {v}{-15}$

$v=(-15)\times {(-3)}$

$v=+45cm$

Thus, the image $v$ is formed at a distance of 45 cm from the convex lens, and the positive $(+)$ sign for image distance implies that the image is placed on the right side of the convex lens.

Now,

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-

$\frac {1}{45}-\frac {1}{(-15)}=\frac {1}{f}$

$\frac {1}{45}+\frac {1}{15}=\frac {1}{f}$

$\frac {1}{f}=\frac {1+3}{45}$

$\frac {1}{f}=\frac {4}{45}$

$f=\frac {45}{4}$

$f=+11.2cm$

Thus, the focal length $f$ of the convex lens is 11.2 cm.