In the rigorous theory of diffraction by a conducting wedge as developed by Sommerfeld and extended by Pauli, the total field is represented by the terms given by geometrical optics plus a contour integral which represents the diffracted waves. If the faces of the wedge form a dihedral angle of &pgr;/m, m=1, 2, 3 … the contour integral vanishes identically and the solution given by geometrical optics is exact. This prediction has been tested and checked by measurements and calculations of the diffraction patterns of wedges whose dihedral angles were 90° and 30°. The measurements were made at a wavelength of 1.25 cm.