Question

A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate the focal length of the lens.

Answer 1

Given:

Object distance, u = −15 cm

Image is inverted and magnified 3 times, so magnification, m = −3 (Negative signis used because the image is real and inverted)

Applying the magnification formula, we get:

m = `v/u`

`-3 = v/(-15)`

v = −3 × (−15)

v = 45 cm

Applying the lens formula, we get:

`1/v - 1/u = 1/f`

`1/45- 1/(-15) = 1/f`

`1/45 + 1/15 = 1/f`

`(1+3 )/45 = 1/f`

`1/f = 4/45`

f = `45/4`

f = 11.25 cm

Hence, the focal length of the lens is 11.25 cm.