  Maxwell's boundary conditions (MBCs) were long known insufficient to
determine the optical responses of spatially dispersive medium. Supplementing
MBCs with additional boundary conditions (ABCs) has become a normal yet
controversial practice. Here the problem of ABCs is solved by analyzing some
subtle aspects of a physical surface. A generic theory is presented for
handling the interaction of light with the surfaces of an arbitrary medium and
applied to study the traditional problem of exciton polaritons. We show that
ABCs can always be adjusted to fit the theory but they can by no means be
construed as intrinsic surface characteristics, which are instead captured by a
\textit{surface response function} (SRF). Unlike any ABCs, a SRF describes
essentially non-local boundary effects. Methods for experimentally extracting
the spatial profile of this function are proposed.
