Question

A convex lens forms a real image 4 times magnified when placed at a distance of 6 cm from the lens. Calculate the focal length of the lens.

Answer 1

Magnification (m) = 4

Distance of the object from the lens (u) = −6 cm

Distance of the image from the lens (v) = ? (to be calculated)

Focal length of the lens (f) = ? (to be calculated)

\[ \text{Applying, } m = \frac{v}{u}\]

\[\Rightarrow \ 4 = \frac{v}{6}\]

v = 4 × 6

∴ v = 24 cm

As the image is real, therefore v = +24 cm

\[ \text{Applying, } \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

\[ \Rightarrow \ \frac{1}{24} - \frac{1}{-6} = \frac{1}{f} \]

\[\Rightarrow \ \frac{1}{f} = \frac{1 + 4}{24}\]

\[\Rightarrow \ \frac{1}{f} = \frac{5}{24}\]

\[\ f = \frac{24}{5}\]

∴ f = 4.8 cm

Thus the focal length of the lens is 4.8 cm.