A concave lens of 20 cm focal length forms an image 15 cm from the lens. Compute the object distance.

Focal length of concave lens, $f$ = $-$20 cm   (focal length of a concave lens is always taken negative)

​Image distance, $v$ = $-$15 cm                          (image distance is taken negative because image formed by a concave lens is on the left side of the lens)

To find: Object distance $(u)$.

Solution:

From the lens formula, we know that-

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

Substituting the given values in the formula, we get-

$\frac {1}{(-15)}-\frac {1}{u}=\frac {1}{(-20)}$

$-\frac {1}{15}-\frac {1}{u}=-\frac {1}{20}$

$\frac {1}{u}=\frac {1}{20}-\frac {1}{15}$

$\frac {1}{u}=\frac {3-4}{60}$

$\frac {1}{u}=\frac {-1}{60}$

$u=-\frac {1}{60}$

$u=-60cm$

Thus, the object is at a distance of 60 cm from the concave lens, and the negative sign implies that it is on the left side of it.