A convex mirror used as a rear-view mirror of a car has a focal length of 2 m. If a bus is located at a distance of 3 m from the mirror, where will its image be formed?

Correct option is A

The correct answer is (a) 1.2 m behind the mirror.

The mirror formula is given by:

​$$\frac{1}{f} = \frac{1}{v}+\frac{1}{u}$$​​

Where:

• f is the focal length of the mirror (f=+2 m, since it is a convex mirror),
• u is the object distance (u=−3 m , negative as the object is in front of the mirror),
• v is the image distance (to be calculated).

Rearranging the formula for v:

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

Substitute the values:

​$$\frac{1}{v} = \frac{1}{2} - \frac{1}{-3} \\ \ \\\frac{1}{v} = \frac{1}{2} + \frac{1}{3} \\ \ \\\frac{1}{v} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \\ \ \\v = \frac{6}{5} = \bf 1.2 \, m \quad \text{ (positive, indicating the image is behind the mirror)}$$​​

Since the bus is behind the mirror:

The image is formed 1.2m behind the mirror, making (a) the correct choice.