  Recent years have seen considerable research success in the field of dynamic
homogenization which seeks to define frequency dependent effective properties
for heterogeneous composites for the purpose of studying wave propagation.
There is an approximation involved in replacing a heterogeneous composite with
its homogenized equivalent. In this paper we propose a quantification to this
approximation. We study the problem of reflection at the interface of a layered
periodic composite and its dynamic homogenized equivalent. It is shown that if
the homogenized parameters are to appropriately represent the layered composite
in a finite setting and at a given frequency, then reflection at this special
interface must be close to zero at that frequency. We show that a comprehensive
homogenization scheme proposed in an earlier paper results in negligible
reflection in the low frequency regime, thereby suggesting its applicability in
a finite composite setting. In this paper we explicitly study a 2-phase
composite and a 3-phase composite which exhibits negative effective properties
over its second branch. We show that based upon the reflected energy profile of
the two cases, there exist good arguments for considering the second branch of
a 3-phase composite a true negative branch with negative group velocity. The
results open intriguing questions regarding the effects of replacing a
semi-infinite periodic composite with its Bloch-wave (infinite domain) dynamic
properties on such phenomenon as negative refraction.
