Question

The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm. The focal length of the lens used is __________ cm.

Answer 1

Let the object distance be $u$, and the image distance be $v$. Since the magnification $m = -\frac{v}{u} = 3$, we have:

$v = 3u$

From the lens formula:

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

Substituting $v = 3u$:

$\frac{1}{f} = \frac{1}{3u} - \frac{1}{u}$

Simplifying:

$\frac{1}{f} = \frac{1 - 3}{3u} = -\frac{2}{3u}$

Now, since $u = 10 \, \text{cm}$, we get:

$f = 15 \, \text{cm}$

Thus, the correct answer is 15.