Bragg law
/ BRAG LAW /
Imagine sunlight bouncing off a stack of glass shelves. Light reflects off the top shelf and also off the ones below it. If the shelves are spaced just right, the reflected beams march in perfect step and add up into a strong bright reflection; spaced wrong, they fall out of step and cancel. Bragg's law is the simple rule that tells you exactly which spacings and angles give that strong reinforcement.
In a crystal the 'shelves' are evenly spaced planes of atoms. A wave reflecting off a deeper plane travels a little farther than one reflecting off the plane above. When that extra travel distance equals a whole number of wavelengths, the reflected waves reinforce. Written out, the condition is that twice the plane spacing times the sine of the glancing angle equals a whole number of wavelengths. Hit that angle and you get a bright spot; miss it and you get darkness.
This matters because it turns a measured angle straight into a distance between atomic planes — it is the workhorse equation behind nearly every crystal-structure measurement, earning William and Lawrence Bragg the 1915 Nobel Prize. An honest caveat: the picture of waves 'reflecting off planes' is a convenient fiction. Atoms scatter waves in all directions; Bragg's law just captures the special directions where those scattered waves happen to add up, and it gives the same answer as the more rigorous reciprocal-lattice treatment.
Shine X-rays of a known wavelength on a table-salt crystal and slowly rotate it. At one precise angle the detector lights up brightly. Plug that angle into Bragg's law and out comes the spacing between the salt's atomic planes — about a quarter of a nanometre — without ever touching a single atom.
One measured angle plus a known wavelength gives the distance between atomic planes.
Bragg's law tells you where a spot can appear, but not how bright it is. A spot allowed by Bragg's law can still be completely dark if the atoms inside each repeat unit happen to cancel — that brightness is governed by the structure factor.