4.9.5 Young Double-Slit Experiment

• 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

Wave Nature of Light

• Interference is a confirmation of the wave-nature of light
• Newton initially proposed that visible light is a stream of microscopic particles called corpuscles
  • However, these corpuscles could not explain interference or diffraction effects, therefore, the view of light as a wave was adopted instead

• Not long after, Huygens came up with the original Wave Theory of Light to explain the phenomena of diffraction and refraction
  • This theory describes light as a series of wavefronts on which every point is a source of waves that spread out and travel at the same speed as the source wave
  • These are known as Huygens’ wavelets

Huygen's wavelets shown by two wavefronts AB and CD

• The fringe width, wavelength of the light, distance between the slits or the distance from the slits to the screen can be calculated using the double-slit equation:

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

• This equation is only when a << D
• 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

• A monochromatic light source makes these fringes clearer and the distance between fringes is very small due to the short wavelength of visible light