  The reflectivity of low energy electrons from graphene on copper substrates
is studied both experimentally and theoretically. Well-known oscillations in
the reflectivity of electrons with energies 0 - 8 eV above the vacuum level are
observed in the experiment. These oscillations are reproduced in theory, based
on a first-principles density functional description of interlayer states
forming for various thicknesses of multilayer graphene. It is demonstrated that
n layers of graphene produce a regular series of n-1 minima in the reflectance
spectra, together with a possible additional minimum associated with an
interlayer state forming between the graphene and the substrate. Both (111) and
(001) orientations of the copper substrates are studied. Similarities in their
reflectivity spectra arise from the interlayer states, whereas differences are
found because of the different Cu band structures along those orientations.
Results for graphene on other substrates, including Pt(111) and Ir(111), are
also discussed.
