wave reflection

In this situation, I think it helps to imagine a spherical wave as many rays being shooted from a point source. You can draw the reflected ray for each of these rays that hit the object. After you do that, you can draw the wave's front by doing the following:

1) Mark a point on each ray which corresponds to a selected distance "t" along the ray (the distance starts counting from the source of course)
2) Join all these points with a line.

So while you increase "t" and redraw, you will be seeing the wave's propagation. I hope this makes sense..

Just trying to sketch what you suggested to see if a pattern emerges.

I'm struggling to picture the reflected rays, because shouldn't they reflect off the spherical object as the spherical waves they approached at? With the difference now being that the reflected spherical waves now have a new (imaginary) point source. If this is correct shouldn't the centre of the spherical object be this new point source? The reason i say this is because the object is a sphere (symmetry all over it).

If the reflected rays' extensions (I don't know if this is the correct word), or the reflected rays themselves all cross each other at the same point, then that point is the new imaginary point source. This holds in special cases though, such as wave from a point source hitting a flat wall. For the case of rays hitting a spherical reflector, I think this won't hold, as the reflected rays' extensions' crossings will lie on a line. In this case the single imaginary source lying somewhere on that line would be an approximation and you would need many smaller sources to have an accurate simulation. I couldn't find a google image that depicts this though...