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Summary

3.1 Young's Double-Slit Interference

  • Young’s double-slit experiment gave definitive proof of the wave character of light.
  • An interference pattern is obtained by the superposition of light from two slits.

3.2 Mathematics of Interference

  • In double-slit diffraction, constructive interference occurs when dsinθ=mλ(form=0,±1,±2,±3)dsinθ=mλ(form=0,±1,±2,±3), where d is the distance between the slits, θθ is the angle relative to the incident direction, and m is the order of the interference.
  • Destructive interference occurs when dsinθ=(m+12)λform=0,±1,±2,±3,…dsinθ=(m+12)λform=0,±1,±2,±3,….

3.3 Multiple-Slit Interference

  • Interference from multiple slits (N>2N>2) produces principal as well as secondary maxima.
  • As the number of slits is increased, the intensity of the principal maxima increases and the width decreases.

3.4 Interference in Thin Films

  • When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180°180° phase change (or a λ/2λ/2 shift) occurs.
  • Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.

3.5 The Michelson Interferometer

  • When the mirror in one arm of the interferometer moves a distance of λ/2λ/2 each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe.
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