Optical Interference
Because the frequency of light waves (~1014 Hz) is too high to be detected by currently available detectors, it is possible to observe only the intensity of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point r is:
where A represents the magnitude of the displacement, φ represents the phase and ω represents the angular frequency.
The displacement of the summed waves is
The intensity of the light at r is given by
This can be expressed in terms of the intensities of the individual waves as
Thus, the interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2π. If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity.
The two waves must have the same polarization to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to a wave of a different polarization state.
Read more about this topic: Interference (wave Propagation)
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—William Howard Taft (1857–1930)