Diffraction is not only a fascinating phenomenon for physicists to
marvel about but it is in fact the only way we have to determine
the atomic structure of solids. In solids atoms are spaced by distances
of order 
m and it is not possible to
resolve the atomic locations using a conventional microscope. Instead
we use diffraction of
waves that have wave lengths of order the
atomic spacing. Electromagnetic
waves with such short wave lengths are called X-rays. When X-rays illuminate a
crystal each atom subject to the radiation becomes a point source of
X-rays as it oscillates in synchronization with the local electric field
from the incident X-ray beam. Constructive and destructive interference
occurs only under the very special conditions wherein
X-rays reflected by a finite fraction of atoms in the crystal add in phase.
Fig. 3 shows a situation in which waves from all atoms
undergo constructive interference.
The lines tilted lines shown
signify normals to the wave fronts of the incident and scattered
X-ray beams. The path difference for these beams is
The condition for constructive interference is thus
Thus from measuring the diffraction angles when X-rays reflect from
a periodic crystal structure we can determine the spacing
between atoms in solids. I show examples of X-ray diffraction from
a single crystal (Laue diffraction with ``white'' X-ray beam)
and neutron diffraction from a sample with a large number of
crystals oriented at random.