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 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