Why find the highest order maxima/minima in slit equations?

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I have been seeing interference and diffraction problems involving the double slit and single slit equations that ask for things like the "highest order maxima" or minima, which I have learned are basically found by setting the angle to 90 degrees. My question is are there any real world applications of this problem? In the lab it is nearly impossible to detect a maxima or minima at 90 degrees unless you have a highly sensitive photodetector. Is this a problem typically encountered in particle physics where you are worried about radiation perpendicular to the beam path?
 

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Charles Link
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I think they are trying to teach a concept that the number of primary maxima are very finite. In a typical diffraction grating spectrometer that works in the visible, you may observe 4 or 5 orders of spectral lines. In any case, the highest order normally appears somewhat short of 90 degrees.
 
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hutchphd
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Diffraction gratings can be blazed to enhance particular diffraction orders. Higher order are sometimes useful (for reasons of geometry, for instance). The behavior of diffracted waves near parallel is also useful for probing surface states of matter.
 
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sophiecentaur
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it is nearly impossible to detect a maxima or minima at 90 degrees unless you have a highly sensitive photodetector
That will be because the pattern of an individual slit (which you multiply by the array pattern for overall pattern) will be zero. Intuitively, you could say that the slit 'looks' narrower and narrower as you increase the angle from the normal.

The reason for working well off axis can be to get greater dispersion, for spectrometry. The lower signal level is just an embarrassment in that case, though.
 

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