3.3.3 Young's Double-Slit Experiment

Two Source Interference

• For two-source interference fringes to be observed, the sources of the wave must be:
  • Coherent (constant phase difference)
  • Monochromatic (single wavelength)

• When two waves interfere, the resultant wave depends on the phase difference between the two waves
  • This is proportional to the path difference between the waves which can be written in terms of the wavelength λ of the wave

• As seen from the diagram, the wave from slit S₂ has to travel slightly further than that from S₁ to reach the same point on the screen
  • The difference in this distance is the path difference

Path difference of constructive and destructive interference is determined by wavelength

• For constructive interference (or maxima), the difference in wavelengths will be an integer number of whole wavelengths
• For destructive interference (or minima) it will be an integer number of whole wavelengths plus a half wavelength
  • n is the order of the maxima/minima since there is usually more than one of these produced by the interference pattern

• An example of the orders of maxima is shown below:

Interference pattern of light waves shown with orders of maxima

•  n = 0 is taken from the middle, n = 1 is one either side and so on

Young's Double Slit Experiment

• Young’s double-slit experiment demonstrates how light waves can produce an interference pattern
• The setup of the experiment is shown below:

Young’s double-slit experiment arrangement

• When a monochromatic light source is placed behind a single slit, the light is diffracted producing two light sources at the double slits A and B
• Since both light sources originate from the same primary source, they are coherent and will therefore create an observable interference pattern
• Both diffracted light from the double slits create an interference pattern made up of bright and dark fringes

• The fringe spacing can be calculated from the interference pattern and the experimental setup
  • These are related using the double-slit equation:

Double slit interference equation with w, s and D represented on a diagram

• The interference pattern on a screen will show as ‘fringes’ which are dark or bright bands
  • Constructive interference is shown through bright fringes with varying intensity (most intense in the middle)
  • Destructive interference is shown from dark fringes where no light is seen

• The distance between fringes is very small due to the short wavelength of visible light
  • A monochromatic light source makes the fringes easier to observe

• If the monochromatic laser light is replaced with a white light source, the interference pattern observed for double slit diffraction is slightly different
• White light is composed of all the colours of visible light, so, each wavelength of white light produces its own interference pattern
• The central fringe is white because, at that position, the path difference for all wavelengths present is zero, therefore all wavelengths will arrive in phase
  • The central fringe is, therefore, the same colour as the source i.e. white

• The first maximum occurs when the path difference is λ
  • Since blue light has a shorter wavelength than red light, the path difference will be smaller, so the blue maximum will appear closer to the centre

• Each colour will produce a maximum in a slightly different position and so the colours spread out into a spectrum

Each fringe appears as a visible spectrum apart from the central white fringe. Red is diffracted the most, violet is diffracted the least