Young's Double-Slit Experiment (AQA A Level Physics)

• Young's double-slit experiment produces a diffraction and an interference pattern using either:
  • The interference of two coherent wave sources 
  • A single wave source passing through a double slit

• The sources of the wave must be:
  • Coherent (have a constant phase difference and frequency)
  • Monochromatic (have the same wavelength)
• In this typical set up for Young's double slit experiment:
  • The light source is placed behind the single slit
  • So the light is diffracted, producing two light sources at slits A and B
  • The light from the double slits is then diffracted, producing a diffraction pattern made up of bright and dark fringes on a screen

The typical arrangement of Young's double slit experiment

Diffraction Pattern

• The diffraction pattern from the interference of the two sources can be seen on the screen when it is placed far away
  
  • Constructive interference between light rays form bright strips, also called fringes, interference fringes or maxima, on the screen
  • Destructive interference forms dark strips, also called dark fringes or minima, on the screen

The constructive and destructive interference of laser light through a double slit creates bright and dark strips called fringes on a screen placed far away

Interference Pattern

• The Young's double slit interference pattern shows the regions of constructive and destructive interference:

• • Each bright fringe is a peak of equal maximum intensity
  • Each dark fringe is a a trough or minimum of zero intensity
• The maxima are formed by the constructive interference of light
• The minima are formed by the destructive interference of light

The interference pattern of Young's double-slit diffraction of light

• When two waves interfere, the resultant wave depends on the path difference between the two waves
• The wave from slit S₂ has to travel slightly further than that from S₁ to reach the same point on the screen
  • This extra distance is the path difference

The path difference between two waves is determined by the number of wavelengths that cover their difference in length

• 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
• For the maximum in the interference pattern: 
  • There is usually more than one produced
  • n is the order of the maxima or minima; which represents the position of the maxima away from the central maximum
  • n = 0 is the central maximum
  • n = 1 represents the first maximum on either side of the central, n = 2 the next one along....

• The spacing between the bright or dark fringes in the diffraction pattern formed on the screen can be calculated using the double slit equation:

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

 

• In this experiment:
  • D is much bigger than any other dimension, normally several metres long
  • s is the separation between the two slits and is often the smallest dimension, normally in mm
  • w is the distance between the fringes on the screen, often in cm. This can be obtained by measuring the distance between consecutive maxima or minima.

• The above equation shows that the separation between the fringes will increase if:
  • The wavelength of the incident light increases
  • The distance between the screen and the slits increases
  • The separation between the slits decreases

Dependence of the interference pattern on the separation between the slits. The further apart the slits, the closer together the bright fringes

• If the laser were to be replaced by a non-laser source emitting white light when diffracted by a double slit:
  • The central maximum would be white with dark fringes of destructive interference either side
  • All maxima would be composed of a spectrum
  • The shortest wavelength (violet / blue) would appear nearest to the central maximum
  • The longest wavelength (red) would appear furthest from the central maximum
  • The colours look blurry and further away from the central maximum the fringe spacing gets so small that the spectra eventually merge without any space between them
  • As the maxima move further away from the central maximum the wavelengths of blue observed decrease and the wavelengths of red observed increase
  • The fringe spacing would be smaller and the non-central maxima would be wider

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