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

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Discussion Overview

The discussion revolves around the concept of finding the highest order maxima and minima in interference and diffraction problems, particularly in the context of double and single slit equations. Participants explore the implications of these concepts in real-world applications, especially in laboratory settings and particle physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that the highest order maxima or minima are typically found by setting the angle to 90 degrees, questioning the real-world applications of this approach due to detection difficulties.
  • Another participant suggests that the concept being taught is that the number of primary maxima is finite, with practical observations in diffraction grating spectrometers showing only a few orders of spectral lines.
  • A different viewpoint mentions that diffraction gratings can be blazed to enhance specific diffraction orders, indicating that higher orders can be useful for geometric reasons and probing surface states of matter.
  • It is highlighted that detecting maxima or minima at 90 degrees is challenging without highly sensitive photodetectors, as the individual slit pattern approaches zero at that angle.
  • One participant explains that working off-axis can provide greater dispersion for spectrometry, although it may lead to lower signal levels, which is seen as a drawback.

Areas of Agreement / Disagreement

Participants express differing views on the practical implications of finding highest order maxima and minima, with some emphasizing the limitations of detection at 90 degrees and others discussing the utility of higher orders in specific applications. The discussion remains unresolved regarding the overall significance of these concepts in real-world scenarios.

Contextual Notes

Limitations include the dependence on the sensitivity of photodetectors for detecting maxima or minima and the unresolved nature of the practical applications in particle physics and spectrometry.

Who May Find This Useful

This discussion may be of interest to those studying optics, diffraction, and interference phenomena, particularly in experimental physics and engineering contexts.

FortranMan
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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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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.
 
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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FortranMan said:
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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