THE DIFFRACTION GRATING
Note the path difference is d sinθ = mλ for
constructive interference, where m can be zero, or any positive
or negative integer. Unlike the case of the double slit, the
dispersion of the grating can be large. That is, the angle θ can
be quite large, so that the small angle approximation is usually
not valid. In general, gratings have much greater dispersion
than prisms.
Resolving power of a grating: λ/(Δλ) =
mN. Here m is the order of the spot observed and N is the
total number of slits in the grating illuminated by the
light-source.
An X-ray photon typically has a kinetic energy of
about 1000 eV and a probability wavelength of about 10-10
m, roughly the typical size of an atom. Thus X-rays diffract
strongly from individual atoms or molecules, or individual
layers of atoms in solids. Diffraction of X-ray photons (or
electrons) from crystals or individual molecules produces a
pattern which can be mathematically inverse-transformed to show
the electron density distribution from which the particles
scattered. Using computer programs that calculate the electron
density, based on given atomic arrangements, it is possible to
obtain very detailed information about precisely how atoms are
fitted together in extremely complex crystals or molecules.
Thin Films
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