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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.
Given:
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.
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