Equivalent boundary conditions for an electromagnetic strip grating are used to derive reflection and transmission coefficients for a boundary value problem consisting of three nonconducting media where the strip grating exists at one of the planar boundaries. The results are used to generate data for a number of cases where data and/or theories exist. The theory presented compares favorably with the literature cited for the limiting condition that the period of the grating be small when compared with the free-space wavelength of the radiation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>