Problem: Linear Array of Emitters, Finite Size Effects

  Consider a linear array of N identical radiation sources, placed at positions . Each source emits radiation at frequency , wavenumber k, amplitude A and the sources are coherent with zero phase difference. We detect the radiation with intensity (defined as the time-averaged amplitude square) with a detector positioned along the line of the array, far away from the sources.

Assume , but finite. The I(k) function will exhibit peaks of finite width. What are the main peak positions? What will the I(k) function look like in the neighborhood of a main peak? What is the intensity of the detected radiation at the peak position? Estimate the width of this peak. How will the integrated intensity (integrated over k) depend on N?