--- RI332 --- Finite Gratings at High Frequancies: Part I, The Helmholtz equation H. Ammari Abstract: We construct geometric-optics solution to a problem of scattering of the Helmholtz equation by a finite periodic dielectric grating placed on the interface between semi-infinite dielectric media. The first order approximation is the solution of the infinite periodic grating. The whole paper is available as a compressed Postscript file by internet procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100) in the directory pub/RI/1995 under the name ammari_332.sept.ps.gz or by Xmosaic or any other www client via the CMAP www server "http://blanche.polytechnique.fr/"