1. The reflection of an electromagnetic plane wave by an infinite set of plates. I;Carlson, J. F.;Quart. Appl. Math.,1947
2. The reflection of an electromagnetic plane wave by an infinite set of plates. II;Heins, Albert E.;Quart. Appl. Math.,1947
3. If the propagation normal of the incident wave falls to the left of ON, angle 𝛽 is a positive acute angle, while if it falls to the right of ON, the angle 𝛽 is a negative acute angle. The case 𝛽=0 requires separate treatment.
4. At this point we realize that to get more than two reflected waves, the inequalities in sec. 2 have to be modified. As we carry on this modification we find that an indefinite number of reflected waves cannot enter. For example, if 𝛼=𝜋/2, then the inequality for two reflected waves reads \[0 < \frac{1}1 + sin𝜃 < \frac{dk}2𝜋 < { \frac{1}2or\frac{2}1 + sin𝜃or\frac{1}1 - sin𝜃 }\]for 0<𝜃<𝜋/2. This is impossible since 𝑠𝑖𝑛𝜃<1. Hence there is only one reflected wave in this case. The formulation we gave in CH I makes no assumptions as to the form of 𝜓(𝑦,𝑧) to the left of the parallel plates. The convergence study in sec 2, of the present paper gives us conditions for one, two, etc., reflected waves.
5. See CH I, p. 321 for some remarks regarding the present use of the term regular.