Question

An object is placed $50cm$ from a lens produces a virtual image at a distance of $10cm$ in front of the lens. Calculate the focal length of the lens.

Answer 1

Step 1 - Given data

The object distance is $u=-50cm$( The object distance is measured from the optical center to the left side)
The image distance is $v=-10cm$ ( The image formed on the same side as that of the object.)

Step 2 - Formula used
Lens formula is given as,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$.

Where $f$ is the focal length of the lens.

Step 3 - Finding the focal length of the lens.

Substitute the values into the lens formula to find the focal length of the lens.
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{f}=\frac{1}{-10cm}-\frac{1}{-50cm} \\ \frac{1}{f}=\frac{1}{50}-\frac{1}{10} \\ \frac{1}{f}=\frac{-40}{500} \\ \frac{1}{f}=\frac{-4}{50} \\ f=\frac{-50}{4} \\ f=-12.5cm \end{gathered}$$

Hence, the focal length of the lens is $-12.5cm$.