Question

An object when placed in front of a convex lens forms a real image of 0.5 magnification. If the distance of the image from the lens is 24 cm, calculate focal length of the lens.

Answer 1

Magnification (m) = 0.5

Distance of the image from the lens (v) = 24 cm

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

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

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

\[\Rightarrow \ 0.5 = \frac{24}{u}\]

\[ \therefore \ u = \frac{24}{0.5} \]

= 48 cm

As u is always negative for a lens, therefore u = −48 cm.

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

\[ \Rightarrow \ \frac{1}{24} - \frac{1}{-48} = \frac{1}{f}\]

\[\Rightarrow \ \frac{1}{f} = \frac{2 + 1}{48}\]

\[\Rightarrow \ \frac{1}{f} = \frac{3}{48}\]

\[\ f = \frac{48}{3}\]

∴ f = 16 cm

Thus the focal length of the lens is 16 cm.