# 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?

• Simply: the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the wave forms produced. You gave examples of where diffraction occurs but it is the same thing. – Ruben Jan 22 '14 at 6:48
• So then, why does it occur? – user24082 Jan 22 '14 at 6:58
• It is an application of Huygens' principle: if the aperture size is very small, it is as if only one point on the wavefront will act as a source of waves and these will be circular. This makes the wave spread (if instead the aperture is large, then many points on the wavefront will act as sources of secondary waves and these will tend to be planar). – Ruben Jan 22 '14 at 7:44
• The planer-ness of the wave grow much more rapidly than the length of the slit, then? – user24082 Jan 22 '14 at 7:48
• I'm afraid I don't understand what you mean. – Ruben Jan 22 '14 at 7:52

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.

Trying to sum up the comments and discussions from @Ruben and @Anthony. One has diffraction and interference. Diffraction may occur upon reflection or by passing a slit. The point is (as you mentioned) that the size of the slit or reflecting object is of the order of the wavelength. In this case one has to consider the wave nature of light and simple geometric optic is not sufficient any more. A simple way of seeing it is actually the mentioned Huygens' principle. Every point of a wave is at any time source of a new elementary wave. If you construct a plane wave like this (see standard text books) it stays a plane wave. According to Huygens the plane wave, hence, is a permanent interference of all these elementary waves. If you confine it to a single source you get a spherical wave. If you have a grating and look at the interference pattern, the important geometrical magnitude is the optical path difference. So at first glance the slit size (or size of your reflecting object) is not so important. But then it is for two reasons. If the slits are broad, different positions contribute with different optical path differences and the effect smears out. Secondly, if your original light source is not coherent (a Laser would be) you need to create coherent light. This is typically done by the slits. The more coherent your original light source the broader you can make the slits. Note, in a laser (a very very coherent light source) you will always see diffraction rings from the aperture. (Bessel rings actually) From this point of view, one has to review the things said above. Most of the time you would say that objects must be of the order of the wavelength, but it is more the coherence length actually, i.e. over which length the elementary waves oscillate with the same phase. In summary and simplified: Diffraction is the wave behavior of light (and the corresponding failure of geometric optics) when passing objects on the scale of the coherence length.