A diffraction grating has period D, and each element of the grating consists of a pair of narrow slits separated by D/N where N is an integer.
a) Sketch the diffraction pattern when the grating is normally illuminated
b)Calculate the relative intensities $I_n$ of the various diffraction peaks of order n, for the case N=4. Which peaks are forbidden?
c)For the case N=2 show that the solution reduced to that of a simple grating of period D/2.
See step 3 for my full attempt to solve the problem.
The Attempt at a Solution
I am aware that the above solution is incorrect, because I ended up ignoring so many things that the solution equals to the one for a double slit, but superposed on a comb of delta functions. My problem is that I don't know how to write the complete function of the grating as a simple function which one could nicely manipulate. Could someone please point me in the correct direction?
P.s I am aware that my attempt of the solution is not the most clear.
P.s.s Link to the higher resolution picture here.