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Interference

 

Diffraction is a specific form of electromagnetic (EM) interference. The classic example of interference is Young's experiment.

[Young's experiment]

A light source is first restricted by a single pinhole, P0, and then by two equidistant pinholes, P1 and P2, and the result observed on a screen. While Young used pinholes, today we normally use slits to make the interference pattern easier to see.

[Interference pattern]

Several things are observable in the pattern on the screen obtained using a white light source:

  • the central vertical line is white, indicating no colour (wavelength) separation there
  • a single colour (eg, red) forms a series of equally spaced vertical lines on the screen
  • Colours are separated so that longer wavelengths are further from the centre
  • the intensity decreased away from the centre, becomes very low, then increases slightly, before dropping off again.

The overall change in intensity from the centre to the sides of the screen is consistent with a single slit diffraction pattern.

The colour separation and series of vertical coloured  lines is Young's interference. The intensity from the source can be reduced so that individual photons pass through slit P0 and when sufficient number have been measured the same pattern is seen on the screen. The only conceivable interpretation for this phenomenon is that each photon from the source which passes through the first slit P0 must then pass through both slits P1 and P2 before being detected at a point x on the screen. A particle could not do this but an EM disturbance could.

A photon entering pinhole P0 has its spatial location severely restricted. From Heisenberg's uncertainty principle this means its momentum is very much broadened. It therefore leaves the slit, still travelling at the speed of light, but with no preferred direction. It therefore spreads out and adopts nearly spherical symmetry. The "spread-out" disturbance is then restricted in two locations simultaneously by pinholes P1 and P2 so that again the two disturbances exit with no preferred direction.

The two disturbances then reach the screen, but the screen is not capable of responding to part of a photon disturbance. They will therefore be detected as a whole photon at random somewhere on the screen but with a probability at any point equal to the strength of the disturbance at that point.

A photon is an undulating disturbance with a characteristic wavelength. We do not need to know its exact shape, merely that it repeats regularly once each wavelength. Any fixed point on this undulation can be labelled as a 'wavefront'. If the wavefronts of the two disturbances exiting pinholes P1 and P2 arrive at point x at the same time they will create a combined disturbance twice as great as their individual disturbances. There is therefore a strong likelihood that such a strong disturbance would be detected on the screen.

This combined disturbance will repeat as we look along the screen whenever the difference in path length (r1-r2) corresponds to one wavelength. Colours with longer wavelengths (eg, red) will therefore take a longer distance to repeat than shorter wavelengths (eg, blue).

Because of the finite size of the pinholes, the momentum is not completely broadened and so the exiting wavefronts will not be perfectly spherical. There is therefore a limit to how far the slits P1 and P2 can be placed apart.