Optical resolution and the Rayleigh criterion

Every optical instrument has a finite aperture — a lens or mirror with some limited diameter — and light passing through any finite opening diffracts, spreading out slightly rather than travelling in perfectly straight lines. The consequence is unavoidable: even a flawlessly manufactured lens forms the image of a single point source not as a mathematical point but as a small bright disc surrounded by faint rings, called an Airy pattern. This blur has nothing to do with imperfect glass or bad polishing; it is diffraction, a direct consequence of wave optics acting on any beam of finite width, and no amount of manufacturing precision can eliminate it.

That unavoidable disc sets a hard limit on how finely an instrument can distinguish two nearby point sources — two stars close together, two features on a microscope slide. If their two Airy discs sit far apart, they are obviously separate. If they overlap so much that they blur into one blob, they cannot be told apart, however good the rest of the optics. The Rayleigh criterion draws a practical line between these cases: two point sources are considered just resolved when the centre of one source's diffraction pattern falls on the first dark ring of the other's. Closer than that and the two discs blend into an indistinguishable smear; farther apart and they are comfortably separate.

The size of that unavoidable disc shrinks as the aperture grows — a larger aperture diffracts light less severely, producing a tighter Airy pattern and finer resolution. This is precisely why the world's major telescopes keep building ever-larger primary mirrors: not primarily to gather more light, but because a bigger aperture pushes the diffraction limit down, letting the telescope distinguish objects an equally well-manufactured but smaller instrument physically cannot separate, no matter how good its optics are.