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Path Difference and Coherence

To understand interference and diffraction patterns, it is important to understand path difference and coherence.

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  • Interference happens when any two waves are superimposed on one another.
    • But in most cases, this creates a very messy wave pattern.
  • To see a clear interference pattern, we need two waves that are coherent.
  • Coherent means that the two waves must have the same frequency and wavelength, and have a fixed phase relation.
    • Usually this fixed phase relation is zero.
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Path difference

  • The path difference between two waves is the difference in length travelled by the waves to get to a certain point.
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Path difference and interference

  • For two coherent wave sources:
  • If the path difference is a multiple of λ, the waves will be in phase and we will see constructive interference:
    • Path difference =nλ= nλ
  • If the path difference is a whole number plus a half λ, the waves will be exactly out of phase and we will see destructive interference:
    • Path difference =(n+12)λ= (n+\frac{1}2)\lambda

Young's Double-Slit Experiment

Young's famous double-slit experiment deals with the interference from two monochromatic, coherent sources. Monochromatic means all light is of the same wavelength.

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Producing coherent waves

  • To observe interference between two waves, we need two coherent sources.
  • We can use two separate sources for this - but it is often tricky to make sure they are coherent.
  • A useful trick is to shine a laser through two slits.
    • The laser produces monochromatic, coherent light.
    • The two slits then act like two identical sources of laser light.
    • The slits must have the same size and be comparable to the wavelength of the laser light to diffract it.
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Experiment layout

  • The diagram shows the production and interference of two coherent, monochromatic light waves.
  • This produces a series of light and dark fringes corresponding to constructive and destructive interference.

Fringes in Young's Double Slit Experiment

We can calculate the spacing of fringes seen in the double-slit experiment.

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Fringe spacing

  • To calculate the spacing between bright fringes in the double-slit experiment, use the following equation:
    • w=λDsw = \frac{\lambda D}{s}
      • Where the fringe spacing is w, the wavelength is λ, the spacing between slits is s, and the distance from the slits to the screen is D.
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Average over many fringes

  • Normally, the fringe spacing is very small.
    • To ensure our measurement is accurate we measure across lots of fringes and divide by the number of fringe widths to find an average.
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Using white light

  • We can use white light instead of laser light in a double slit experiment.
  • Instead of clear bright and dark fringes:
    • The middle fringe is just bright white light.
    • All fringes are more spread out.
    • Side fringes have a spectrum of visible colours. Blue light diffracts less than red so is nearer the centre of the screen.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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