Question

An object is placed perpendicular to the principal axis of a convex mirror of a focal length of 10 cm. The distance of the object from the pole of the mirror is 10 cm. Find the position of the image formed.

Answer 1

Step 1: Given data

The focal length of the mirror, $f=10cm$

Object distance, $u=-10cm$ (object distance is always taken negatively as it is on the left side)

Step 2: Finding the image distance using the mirror formula

From the mirror formula, we know that

$$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}+\frac{1}{-10}=\frac{1}{10} \\ \frac{1}{v}–\frac{1}{10}=\frac{1}{10} \\ \frac{1}{v}=\frac{1+1}{10} \\ \frac{1}{v}=\frac{2}{10} \\ \frac{1}{v}=\frac{1}{5} \\ v=+5cm \end{gathered}$$

Thus, the position of the image is 5 cm from the lens, and the positive sign (+) implies that it forms behind the lens (on the right side).