Question

A concave lens of 20 cm focal length forms an image 15 cm from the lens. Compute the object distance.

Answer 1

Focal length of concave lens f = - 20 cm (focal length is negative for a concave lens)
Image distance v = - 15 cm ( negative sign is given because the image formed by a concave lens is on the left side of the lens)
Using the lens formula:

$$\begin{gathered} \frac{\text{1}}{\mathit{\text{f}}}\mathit{=}\frac{\text{1}}{\mathit{\text{v}}}\mathit{-}\frac{\text{1}}{\mathit{\text{u}}} \\ \Rightarrow \frac{\text{1}}{\text{-20}}=\frac{\text{1}}{\text{-15}}-\frac{\text{1}}{\mathit{\text{u}}} \\ \Rightarrow \frac{\text{1}}{\mathit{\text{u}}}=\frac{\text{1}}{\text{20}}+\frac{\text{1}}{\text{(-15)}} \\ \Rightarrow \frac{\text{1}}{\mathit{\text{u}}}=\frac{\text{3-4}}{\text{60}}=-\frac{\text{1}}{\text{60}} \end{gathered}$$

∴ u = - 60 cm.

The negative sign shows that the object is on the left side of the concave lens.
Therefore, the object is at a distance of 60 cm and on the left side of the concave lens.