A ray of light entering through the pole of a concave lense emerges without deviation; why?

A convex lens is a converging lens, meaning that light
rays entering the lens parallel to its axis are converged as they pass through the
lens.  When they come out the other side of the lens they will strike the focal point
behind the lens.  The process by which the lens bends the light rays is called
refraction.

A concave lens is a diverging lens.  Light rays
are refracted so that they diverge as they pass through the
lens.

For either lens type the refraction is caused by the
angle between the light ray and the surface of the lens.  The greater the curvature of
the lens, the greater the angle between the ray and lens surface (angle of
incidence).

At the pole (axis) of the lens the lens surface
is exactly perpendicular to the light path, representing a zero incidence angle.  The
ray will simply pass through the lens without refraction (bending) and continue out the
lens to pass through the focal point, regardless of the distance of the focal point
behind the lens.  It is only the light rays that are off center from the lens’s axis
that are bent.  They will be angled in a way to converge on the focal point behind the
lens.

These concepts are illustrated in the upper left
diagram on the first page of the reference.  One can see what happens to the light ray
passing straight through the lens’s axis (pole), versus the rays above and below the
axis that are bent by the lens as they go through.