Electromagnetic (EM) field intensities happen to exist as solutions of Maxwell’s equations in a three dimensional space. In the present paper an attempt has been made to determine the components of EM field intensities belonging to a pair of groove regions adjacent to a convex triangular prism. Field intensities are supposed to be longitudinal symmetry and the triangular prism forms a part of an echellete grating of fixed period. Two existence theorem regarding longitudinal symmetric electric intensity vector and magnetic intensity vector associated with time dependent spherical wave have been established. Finally, the expression for the current density associated with the prism has been derived.