$A$ convex mirror used on an automobile has $3\, m$ radius of curvature. If a bus is located at $5\, m$ from this mirror,find the position,nature,and size of the image.

(N/A) Given: Radius of curvature $R = +3\, m$,Focal length $f = R/2 = +1.5\, m$.
Object distance $u = -5\, m$.
Using the mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$.
Substituting the values: $\frac{1}{1.5} = \frac{1}{v} + \frac{1}{-5}$.
$\frac{1}{v} = \frac{1}{1.5} + \frac{1}{5} = \frac{5 + 1.5}{7.5} = \frac{6.5}{7.5}$.
$v = \frac{7.5}{6.5} \approx +1.15\, m$.
The image is formed at $1.15\, m$ behind the mirror.
Magnification $m = -\frac{v}{u} = -\frac{1.15}{-5} = +0.23$.
Since $v$ is positive,the image is virtual and erect. Since $m < 1$,the image is diminished (smaller in size) by a factor of $0.23$.