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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.