Answer:
When light rays after reflecting from the mirror gets diverge and do not intersect at a point in the space then it will assumed that the light ray will intersect at imaginary point behind the mirror.
That imaginary point from which light appears to originate after reflection from the mirror is known as virtual image.
In case of convex mirror for all positions of object the image will be virtual image.
As we know by mirror formula
[tex]\frac{1}{d_i } + \frac{1}{d_o} = \frac{1}{f}[/tex]
now here we will have
[tex]\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}[/tex]
now we know that focal length of convex mirror is always positive as well as object position is always negative so here image will always form behind the mirror as per above formula.
So this will be virtual image always due to convex mirror
