Interference



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                 Interference, pattern produced by the superposition of two waves. It follows the principle of the superposition principle. Indeed the entire field of interference is based on the superposition principle according to which at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves.

Consider two needles S1 and S2 moving periodically up and down in an identical fashion in a trough of water. They produce two water waves, and at a particular point, the phase difference between the displacements produced by each of the waves does not change with time; when this happens the two sources are said to be coherent. Consider a point P for which S1P = S2P.

Since the distances S1P and S2P are equal, waves from S1 and S2 will take the same time to travel to the point P and waves that emanate from S1 and S2 in phase will also arrive, at the point P, in phase.

Thus, if the displacement produced by the source S1 at the point P is given by

y1 = a cos ωt

then, the displacement produced by the source S2 (at the point P) will also be given by

y2 = a cos ωt

Thus, the resultant of displacement at P would be given by

y = y1 + y2 = 2 a cosωt

Since the intensity is the proportional to the square of the amplitude, the resultant intensity will be given by

I = 4 I0