Q.What is a wavefront? How is it related to rays of light? What is the shape of the wavefront at a point far away from the source of light?

[!TLDR] A wavefront is the locus of points sharing the same phase at one instant; rays are simply the lines perpendicular to the wavefront everywhere, pointing along the propagation direction; far from a point source, the wavefront becomes effectively PLANE. [!ANSWER] A wavefront (locus of same-phase points) is always perpendicular to the rays at every point; far from a source it flattens into a plane wavefront.

A wavefront is defined as the locus of all points that share the same phase -- the same state of oscillation and the same distance travelled from the source -- at a given instant of time; equivalently, it is the set of points that light starting simultaneously from the source has reached together at that instant. Its relation to rays is direct and simple: a RAY, in ordinary ray/geometrical optics, is exactly the direction along which light energy is actually propagating at any point, and this direction is always PERPENDICULAR to the wavefront at that point -- for a point source's spherical wavefronts, the rays are simply the radii of the sphere, pointing straight outward from the source; for a plane wavefront, the rays are all parallel to one another. As the distance from a point source grows very large, a small local patch of its (still, technically, spherical) wavefront becomes indistinguishable from a flat plane -- exactly as Earth's curved surface looks locally flat to someone standing on it -- so at a point far away from the source, the wavefront shape is a PLANE wavefront (a plane wave), with all its rays effectively parallel to each other rather than visibly diverging. [!ANSWER] A wavefront (locus of same-phase points) is always perpendicular to the rays at every point; far from a source it flattens into a plane wavefront.

State the phase-based definition of a wavefront, note that rays are always perpendicular to it (the propagation direction at each point), and apply the far-field/local-flatness argument to identify the shape at large distance as a plane wavefront.

Describing a wavefront simply as 'the path of light' (confusing it with a ray, its own perpendicular partner) rather than correctly identifying it as the surface/locus of equal phase.