Why Do Some Diffraction Orders Go Missing?

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SUMMARY

The phenomenon of missing diffraction orders occurs in double and n-slit diffraction due to the overlap of interference and diffraction patterns. Specifically, when the zeros of the sinc function (representing diffraction intensity) coincide with the maxima of the cosine function (representing interference intensity), the corresponding order of diffraction becomes invisible. This relationship highlights that interference is influenced by the distance between slits, while diffraction is determined by the width of the slits.

PREREQUISITES
  • Understanding of double and n-slit diffraction concepts
  • Familiarity with interference patterns and their mathematical representation
  • Knowledge of the sinc function and its properties
  • Basic principles of wave optics
NEXT STEPS
  • Study the mathematical derivation of the sinc function in diffraction
  • Explore the impact of slit width on diffraction patterns
  • Investigate the relationship between slit distance and interference maxima
  • Read about advanced topics in wave optics, such as Fraunhofer diffraction
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Students and professionals in physics, particularly those specializing in optics, as well as educators looking to enhance their understanding of diffraction phenomena.

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Explain the concept of missing orders in case of double and n slit diffraction.
 
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We say that an order of diffraction is missing if it disappears as a consequence of the overlapping of the interference and the diffraction patterns.

On a screen, intensity from interference has all its maxims at the same level (like a cosine), while intensity for diffraction goes like a sinc (sin(x)/x), so that it gradually tends to 0. The sinc has several zeros (when sin(x)=0 except from x=0), and if one of these zeros overlaps a maximum of interference, we see nothing.
So, there is missing order.

Interference depends on the distance between the slits, while diffraction depends on the width of the slits.

For more info, you can read http://en.wikipedia.org/wiki/Double_slit
 
We say that an order of diffraction is missing if it disappears as a consequence of the overlapping of the interference and the diffraction patterns.

On a screen, intensity from interference has all its maxims at the same level (like a cosine), while intensity for diffraction goes like a sinc (sin(x)/x), so that it gradually tends to 0. The sinc has several zeros (when sin(x)=0 except from x=0), and if one of these zeros overlaps a maximum of interference, we see nothing.
So, there is missing order.

Interference depends on the distance between the slits, while diffraction depends on the width of the slits.

For more info, you can read http://en.wikipedia.org/wiki/Double_slit
 

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