Particles scatter incident rays in all directions. In some of these
directions the scattered beams are in phase and reinforce each other to give diffracted
beams i.e. constructive interference. The mathematical description of diffraction was
first written down by von Laue in 1912 and his equations are still useful. However, a
simpler way to describe the geometry (but not intensity) of diffraction is using Bragg's
law.
Single layer of atoms
Consider first a single plane of regularly spaced atoms:
Imagine a beam of coherent light is incident on the atoms at an angle qIN. Some of the rays interact with the
atoms and are scattered in all directions. (Most of the rays are transmitted.)
Consider the two scattered waves, A and B. They are in phase, reinforcing each other to give a
diffracted beam, only when they travel the same distance, i.e. when x
= y. This
only occurs for scattered waves with an outgoing angle of:
- qOUT = qIN
Thus a diffracted beam from a single row of atoms is made up of all the waves
which are scattered with an outgoing angle equal to the incoming angle of the incident
waves. This is true for incident waves of any wavelength.