Question

A convex lens produces a real and inverted image 2.5 times magnified at a distance of 25 cm from the lens. Calculate focal length of the lens.

Answer 1

Magnification (m) = 2

Distance of the image from the lens (v) = 25 cm

Distance of the object from the lens (u) = ? (to be calculated)

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

Applying,

\[ m=\frac{v}{u} \quad \Rightarrow 2.5=\frac{25}{u} \]

∴ \[ u=\frac{25}{2.5}=10 \mathrm{~cm} \]

As u is always negative for a lens, therefore u = −10 cm.

Applying,

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

⇒ \[ \frac{1}{25}-\frac{1}{-10}=\frac{1}{f} \Rightarrow \frac{1}{f}=\frac{2+5}{50}=\frac{7}{50} \]

∴ \[ f=\frac{50}{7}=7.14 \mathrm{~cm} \]

Thus the focal length of the lens is 7.14 cm.