A hint is that it depends on the size ## d ## which is often many times the wavelength for the case of just two slits, but typically is on the order of a wavelength for the spacing of the slits or lines in a diffraction grating. That isn't always the case, but it seems to be the assumption that you need to make here. (Edit: See the 3rd paragraph below for additional comments on this). ## \\ ## An item of interest here is the intensity peaks from a multi-slit or multi-line grating are narrower in the resulting ## \Delta \theta ## than the intensity peaks from a two-slit pattern, where for a grating with many slits or lines the intensity peak can be very narrow in the angular spread ## \Delta \theta ##. You can see this in the figures above where for even 5 slits, the intensity peaks are narrower than for the two-slit case in the appearance on the screen. For the two slit case, each of the peaks is a wide blob. For the 5 slit case, the bright red region of each intensity peak is a narrower stripe. This is not why the small angle approximation can not be used for a grating though. ## \\ ## The question doesn't seem to be what I would call a very accurate question. In addition, the more important feature of the difference between the double-slit and multi-slit or multi-line grating result is the more narrow intensity peaks that result. The "small angle" approximation does still apply for both the double slit and multi-slit or multi-line grating at small angles, and starts to break down as ## \theta ## gets larger for both cases. For this reason, I think the question really misses the boat.
