A converging lens has focal length of $12cm$, Calculate at what distance should the object be placed from the lens so that it forms an image at $48cm$ on the other side of the lens.

Step 1: Given data

The focal length of a converging lens is $f=+12cm$( Focal length of a converging lens is positive)

Image distance, $v=+48cm$( Distance measured on the right side of the optical center is positive)

Step 2: Formula used

From the lens formula,

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

where $u$is the object distance.

Step 3: Finding the object's distance

Substitute the values into the formula.

$$\begin{gathered} \frac{1}{12cm}=\frac{1}{48cm}-\frac{1}{u} \\ \frac{1}{u}=\frac{1}{48}-\frac{1}{12} \\ \frac{1}{u}=\frac{1-4}{48} \\ u=\frac{48}{-3} \\ u=-16cm \end{gathered}$$

To form an image at $48cm$ on the right side of the converging lens of focal length $12cm$, the object should be placed at $16cm$ on the left side of the lens.