What is Diffraction?

Diffraction is just light interacting with small objects, and bending, but this seems like a very imprecise definition to me. What is diffraction, actually? I was confused because there are at least two diffraction gratings, that I know of. One being actually slits, through the standard diffraction I learned about in class, and then there are spaced grooves which can also diffract. This latter one, I thought, would just be reflection and interference, but I was told it's the same phenomenon. So again, what is diffraction?

Answer

Don't get too worried about fine meanings of the word: it is ultimately a little imprecise, and when you're thinking about real, physical problems, you're going to be working with equations.

The more fundamental concept is interference, which is simply a manifestation of the linear superposition principle. Amplitudes add, so magnitude and phase is important when summing up contributions to a field from different sources.

Diffraction works like this. Suppose you know a monochromatic field's values on one transverse plane. Now Fourier transform the values, to express the field on a transverse plane as a sum of plane waves. Plane waves running nearly orthogonal to the transverse plane have almost the same phase over wide transverse regions. So they show themselves as low spatial frequencies in the transverse plane field pattern. Plane waves running at steep angles to the transverse plane beget high spatial frequency components in that plane.

So we've resolved our field into a linear superposition of plane waves. Because these waves are propagating in different directions, they undergo different delays in reaching another transverse plane. The Fourier co-efficients take on different phases, so the same constituent plane waves interfere together to make a different field configuration on other transverse planes.

Diffraction is thus the interference of a field's (e.g. an electromagnetic field following the linear Maxwell equations) plane wave constituents. These constituent plane waves beat differently on different transverse planes because they undergo different phase delays by dint of their different directions. See my answer here and also here for more info.

Another equivalent (in the larger propagation distance limit) is Huygens's principle. Think of a single slit field. Diffraction is the interference on a farfield plane between the different fields arising from the different Huygens point sources at different positions in the slit.