A diffraction grating is a closely spaced array of apertures or obstacles forming a series of closely spaced slits. The simplest type in which an incoming wave front meets alternating opaque and transparent regions (with each opaque/transparent pair being of the same size as any other pair) is called a transmission grating. Determine the angular position of the maxima of such a grating in terms of \(\lambda\) and \(a\), the distance between centers of adjacent slits. If light of 5000 Ȧ  is incident of a slit containing 18,920 slits and of width \(5 \mathrm{~cm}\), calculate the angular position of the second maximum. 

N/2 e-2zik, nd sin[(N + 1)dk] sin[dk] n=-N/2