A convex mirror with a radius of curvature of 3 m is used as the rear-view mirror for a vehicle. If a bus is located at 5 m from this mirror, find the position, nature, and size of the image.

The mirror formula will determine where the image is located. By taking into account the sign and applying the magnification formula, the kind and size of the picture will be indicated.
Given that the bus may be seen at the distance from the convex mirror, $\mathrm{u}=-5\mathrm{m}$
The convex mirror's arc of curvature, $\mathrm{r}=+3$m

the convex mirror's focal length is as a result, $f=+\frac{3}{2}m$
The mirror formula says that
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}$
By entering the values for each term, we obtain
$\frac{1}{\mathrm{v}}+\left(\frac{1}{-5}\right)=\frac{2}{3}$
$\frac{1}{\mathrm{v}}=\frac{2}{3}+\frac{1}{5}$
$\frac{1}{\mathrm{v}}=\frac{10+3}{15}=\frac{13}{15}$
$\therefore \mathrm{v}=\frac{15}{13}\approx 1.1538 \mathrm{m}$

thus the picture is in a favorable position. As a result, the picture will appear behind the mirror, meaning it will be a virtual image.
Now, based on the mirror's amplification formula,

$\mathrm{m}=\frac{{\mathrm{h}}_{\mathrm{I}}}{{\mathrm{h}}_0}=-\frac{\mathrm{v}}{\mathrm{u}}$
On putting the values of v and u, we get
${\mathrm{h}}_{\mathrm{I}}=-\left(\frac{\frac{15}{13}}{-1.5}\right){\mathrm{h}}_0=\frac{10}{13}{ \mathrm{h}}_0$

The nature of the image created by the convex mirror will be upright and decreased since the convex mirror's magnification is positive and smaller than 1.
Because of this, the convex mirror's produced image will be upright, reduced, and virtual, and it will appear 1.1538 m behind the mirror.

Hence, the correct answer is option C.