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

Correct Answer: 15

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.