Question

why focus of a convex mirror is always behind the reflecting surface ?

Answer 1

Dear student
As per your standard, the reason for the focus of convex mirror being behind is that because of it's curvature.
You may have notice that the convex mirror is seems to be a part of sphere whose center lies behind its current aperture. So, it's center is behind the mirror thus it's focus is also behind the mirror.
Moreover, when any rays parallel to principle axis reflected it appears to be coming from a point behind the mirror, that is focus no doubt.
Regards