Question

A concave lens of focal length $20cm$ forms an image at a distance of $10cm$ from the lens. What is the distance of the object from the lens.

Answer 1

Step 1 - Given data.

The focal length $\left(f\right)$ of the lens is $20cm$. As the focal length of a concave lens is negative. Therefore, $f=-20cm$.
The image distance $\left(v\right)$ from the lens is $10cm$. For a concave lens, the image formed is always virtual so the image distance is negative. Therefore, $v=-10cm$.

Step 2 - Formula used.
The object distance $\left(u\right)$ from the lens can be found using the lens formula, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$.

Step 3 - Finding the image distance.

Substitute the values into the lens formula to calculate the image distance.

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{-20}=\frac{1}{-10}-\frac{1}{u} \\ \frac{1}{u}=\frac{1}{20}-\frac{1}{10} \\ \frac{1}{u}=\frac{-10}{200} \\ \frac{1}{u}=\frac{-1}{20} \\ u=-20cm \end{gathered}$$

Hence, the object distance from the lens is $-20cm$. The negative sign indicates that the object is placed in front of the lens.