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Transmission Through a Dim-series Grating (a) The thickness of a thin transparent plate varies sinusoidallv in the x direction, d(1,y) = ed + mailer/AIL as illustrated in Fig. 2.4-11. Show that the complex amplitude transmittance is rte; v) = ManiHm Dicadn conxfa where in} = exp[jtn + llkoo']. (b) Shear that an incident plane wave traveling at a small angle B,- with the z direction is transmitted in the form of a sum of plane waves traveling at angles liq given by (2-4-9)- Hint: Expand the periodic function {(x, y} in a Fourier series