For a particular double-slit apparatus the ratio of slit width to slit separation is fixed at a/d=0.25, and the illumination wavelength is held constant. A student wishes to analyze the intensity pattern produced on a distant screen.
(a) On axes whose horizontal variable is the diffraction angle θ (with the origin at the central maximum) and whose vertical variable is relative intensity, sketch a qualitative graph of the combined diffraction–interference pattern. Clearly label the diffraction envelope and indicate the positions of the first six interference orders (both positive and negative), marking any that are missing.
(b) Provide a detailed explanation for why the missing orders identified in part (a) do not appear, referring to the superposition of wave contributions across an individual slit.
(c) The apparatus is modified so that a/d=1/3. Without performing new calculations from first principles, predict which interference orders will now be absent within the central diffraction envelope and justify your prediction.