Reflection matrices with the correct space-time symmetry properties ma
y be obtained from the standard Maxwell boundary conditions only when
the constitutive relations for the D and H fields satisfy covariance r
equirements. In this paper we present the first application of covaria
nt multipole forms for D and H, to the order of electric quadrupole an
d magnetic dipole, to a magnetic crystal in order to compare the predi
ctions obtained from this theory with recent experimental results. In
particular, the theory is used to determine the Fresnel reflection amp
litudes for antiferromagnetic Cr2O3 when a monochromatic plane light w
ave is incident normally from a vacuum on a crystal face perpendicular
first to the C-3 axis and then to the C-2 axis. The theory agrees wel
l with experiment. In addition, it reveals a novel relationship betwee
n certain components of the frequency-dependent magnetoelectric tensor
, which, with the aid of transmission and reflection data, would enabl
e the surface and bulk contributions in reflection to be distinguished
.