An object is placed at a distance of 60 cm from a concave lens of focal length 30 cm. Use lens formula to find the position of the image formed in this case.

Given,

• Object distance ($\text u$) = -60 cm
• Focal length of the lens ($\text f$) = -30 cm

Here, the negative sign for $\text u$ shows that the object is placed in front of the lens, and the negative sign for $\text f$ shows that the lens is concave (diverging).

By, using the lens formula,

$\dfrac{1}{\text f} = \dfrac{1}{\text v} - \dfrac{1}{\text u} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{\text f} + \dfrac{1}{\text u} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{(-30)} + \dfrac{1}{(-60)} \\[1em] \Rightarrow \dfrac{1}{\text v} = -\dfrac{1}{30} - \dfrac{1}{60} \\[1em] \Rightarrow \dfrac{1}{\text v} = -\dfrac{2 + 1}{60} \\[1em] \Rightarrow \dfrac{1}{\text v} = -\dfrac{3}{60} \\[1em] \Rightarrow \dfrac{1}{\text v} = -\dfrac{1}{20} \\[1em] \Rightarrow \text v = -20 \text { cm}$

Hence, the image is formed in front of the lens at a distance of 20 cm from it.