EXERCISE 2.4-5 Transmission Through a Diffraction Grating. (a) The thickness of a thin transparent plate varies sinusoidally in the direction, d(x, y) = d₁[1+ cos(2x/A)], as illustrated in Fig. 2.4-11 Show that the complex amplitude transmittance is t(x,y) = ho expli½(n - 1)kodo cos(2x/A)] where ho = exp(−j(n + 1)kodo]. (b) Show that an incident plane wave traveling at a small angle 0, with respect to the z direction is transmitted in the form of a sum of plane waves traveling at angles, given by (2.4-12). Hint: Expand the periodic function t(x, y) in a Fourier series. wwwwwww Figure 2.4-11 A thin transparent plate with periodically varying thickness serves as a diffraction grating. It splits an incident plane wave into multiple plane waves travel- ing in different directions. (2.4-12) Grating Equation