Relation between phase difference and path difference is
path difference/wavelength=phase difference/2*pi
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The phase difference between two waves is directly proportional to the path difference between them. The phase difference is a measure of how much the wave has shifted along its oscillation cycle, while the path difference is a measure of the spatial separation between two points where the waves are evaluated.
In constructive interference, the path difference between two waves is an integer multiple of the wavelength, leading to a phase difference of 0 or a multiple of 2π. This results in the waves being in phase and adding up constructively to produce a larger amplitude.
The phase difference between two points on a wave front is the measure of how much the phase of one point lags behind or leads ahead of the phase of another point. It is usually given in radians and depends on the difference in path lengths from the source to the two points. The phase difference is important in understanding interference patterns and wave interactions.
As you move away from the center of the interference pattern, the path length difference between the two interfering waves decreases, resulting in fewer and narrower interference fringes. This occurs because the phase difference between the waves changes gradually with distance from the center, causing the fringes to become closer and thinner.
The waves will be in phase when they combine. Two waves that are in phase have reached corresponding points in their wave cycle, regardless of the path length difference traveled. In this case, the extra two wavelengths traveled by one of the waves will not affect their phase relationship.
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