Light of wavelength 650nm passes through a single slit of width 25μm and is detected by a photodetector that can collect light only within an angular range of ±15∘ measured from the central axis (the axis perpendicular to the slit and passing through its center).
(a) Determine the highest order of diffraction minimum whose angle lies inside the photodetector’s acceptance range on one side of the central axis.
(b) Calculate the total number of dark fringes that the detector can register within its full angular range, counting both sides of the central maximum but not including the central bright region itself.