• waves tend to spread out as they propagate

diffraction

  • variety of wave interference effects during wave propagation

point source

  • a point wave source generates circular waves point-wave-source

aperture source

  • waves splitting through an aperture can be assumed to have several point sources along the plane of the aperture aperture-wave-source

wavefronts

  • several wavefronts are formed at a distance ahead in the propagation path due to interference 9-point-source-aperture

  • the waves get weaker by spreading out as they move away from the aperture diffraction-angle-1 diffraction-angle-2
  • the angle of the spread of the wave is the diffraction angle
    • diffraction angle \( \theta \propto \frac{\lambda}{d} \)
    • where:
      • \( \lambda \): wavelength
      • \( d \): size of aperture opening
  • larger the opening, smaller the diffraction angle and vice-verse
    • lesser the pinching of waves into a point-source like opening

diffraction from periodic structures

  • a diffraction grating is a device with a piece of glass (or other light transmitter) with a set of closely spaced lines scratched onto it
  • crystals naturally have periodically spaced atoms in them
    • crystals are just periodic array of atoms
  • x-rays (and other short wavelength lights) shined through crystals tell us a lot about the crystal structure

periodic scatterers

  • one scatter will give a set of phase fronts called concentric circles

  • multiple equally spaced scatterers give multiple sets of concentric circles

  • these scatterers all add in phase for particular directions
    • ‘straight ahead’ called a zeroth order diffraction
      • straight-ahead
    • also, two more are obtained - ‘upward’ and ‘downward’
      • upward-direction
      • downward-direction
  • at large distances from the scatterer, a multiple beam diffraction pattern in obtained
    • which looks like a set of points on a screen
  • larger scatterer separation gives beams closer in angle
    • three-beams-scattering
    • three-beams-scattering
    • three-beams-scattering
  • the angle \( \theta \) of these diffracted waves is given by simple geometry
    • three-beams-scattering
    • \( \sin \theta = \frac{\lambda}{s} \)
      • \( \lambda \): wavelength
      • \( s \): separation between scatterers
    • larger spacing \( s \) multiple diffraction ‘orders’ are possible
      • \( \sin \theta_1 = \frac{\lambda}{s} \)
        • is a first order diffraction
      • \( \sin \theta_2 = \frac{2\lambda}{s} \)
        • is a second order diffraction
  • generalizing, for a 1D array of scatterers
    • the diffraction angle is \( \theta_n = \sin^{-1}\left( \frac{n\lambda}{s} \right) \)

multiple slits

  • for an electron beam incident on an array of multiple slits
    • you will see a pattern with the same period as that for an array of two slits
  • however, as \(n\) increases, the sharpness of the intensity peaks will increase
    • so the pattern will look more and more like a series of discrete spots