Question

what is the relation between phase difference and path difference

Answer 1

Phase difference and path difference are directly proportional to each other. Path difference is the difference in path covered by two waves while phase difference determines the interference pattern of the waves. The condition of constructive interference is fulfilled when the path difference between 2 waves is integral multiple of wavelengths whereas in destructive interference the path difference between 2 waves is odd multiple of half wavelength. Moreover phase difference can also be defined as the difference between any two reference points in a wave for example sine wave is zero at the origin but cosine wave is pi/2 at the origin so the phase difference is pi/2. The crusts and troughs of two waves will occur at the same time when both the waves have a phase difference of zero.