  This paper describes the use of Feynman photon path integrals to compute the
probability of detecting reflected, diffracted, and scattered photons at
different points in space after interacting with conduction electrons. Five
examples are given: (1) a thin parabolic sheet of conduction electrons (e.g. a
metal mirror) that produces a sharp focus of a distant point source surrounded
by the Airy diffraction pattern, (2) the loss of focusing power as the
thickness of the parabolic sheet is increased and complete destructive
interference for thicknesses that are an integer multiple of 1/2 the
wavelength, (3) diffraction of photons entering a thin sheet from the side, (4)
diffraction of photons entering the side of a sheet as its thickness is
increased, and (5) the angular scattering distribution of internally generated
photons in an extended volume of conduction electrons. The calculations
integrated the complex probability amplitudes for photon paths from (a) a point
source to (b) all points in the conduction electron volume and to (c) a point
detector. At each detector position the detection probability was computed as
the square of the absolute value of the integral. In general, if there is a
concentration of paths that have nearly the same complex amplitude phase,
reflection dominates. Otherwise, if the conduction electron volume has sharp
boundaries, diffraction dominates. Isotropic scattering dominates for
conduction electrons distributed throughout an extended volume, and may explain
how scintillation photons in cryogenic n-type GaAs can escape total internal
reflection trapping, which is essential for its high luminosity.
