In the case that the phase function does not depend on the variable, the velocity becomes In this case, the amplitude and the phase reduce toįrom which the velocity is derived by differentiating the total phase function In the eikonal form the total wavefunction becomes the two interfering wavefronts must intersect at a very small angle, otherwise, the path difference between the interfering waves becomes large and interference fringes will get close to each other and will not be sharp.The guiding equation for the particle velocity is, which is calculated from the gradient of the phase of the wavefunction in the energy representation. The two sources emitting a set of interfering waves should be very close to each other, i.e. The sources should be very narrow – because if the sources are broad, it becomes equivalent to a large number of narrow sources lying side by side and will produce their own interference pattern that disturbs the fringe system. The 2 sets of interfering waves should either have the same phase (or constant phase difference), this can only be possible if both waves originate from a single point source because if they originate from a different then it is difficult to handle the fluctuations. without it we can’t get completely dark or bright fringe) This will reduce general illumination (i.e. The two sources should continuously emit waves of the same wavelength or frequency, this is because the resultant displacement will be constant only if the periodic time is the same.įor obtaining interference fringes, the amplitudes of the two interfering wave trains should be equal or very nearly equal. In short, Interference is the redistribution of light energy obtained by the superposition of 2 or more waves from coherent sources (sources that emit light waves with a constant phase difference and nearly equal amplitude).Ĭondition For Permanent/Good Interference Pattern Of Light The energy missing at one region reappears at another region of the energy distribution of interfering waves, so we can say there’s only redistribution and no destruction and creation of energy in the phenomenon of interference of the waves. In the phenomenon of interference, there’s only a transfer of energy from one region to other. This modification in the distribution of light energy obtained by the superposition of two or more waves is called “interference”.ĭuring the overlap of crest & trough, it should be noted that, While at other points where the crest of one wave falls upon the crest (or trough of one wave falls upon trough) of the other, then the resultant amplitude is increased and the energy becomes maximum. With a single source of disturbance, the distribution of energy in the surrounding medium is uniform, but when two adjacent sources give out continuous waves of the same wavelength and amplitude and have the same phase (or constant phase difference), the distribution of energy is no longer uniform.Īt some points where the crest of one wave falls upon the trough of the other and vice versa, the resultant amplitude is reduced to zero, and energy is minimum. Now let’s move ahead and understand what does “interference” actually means.
To understand – “what is interference?” we first have a little knowledge about the “Superposition Principle”.Īccording to the principle of superposition – when two or more sets of waves pass through & cross each other then the resultant displacement (amplitude) produced by several waves at any instant is the vector sum of the displacement (amplitude) produced by each one of the waves.
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