Write the relation between path difference and phase difference?

Explanation

(i) In the path of the wave, one wavelength `lamda` corresponds to a phase of `2pi`. A path difference `delta` corresponds to a phase difference `phi` as given by the equation,
` delta = (lamda)/(2pi) xx phi " or " phi = (2pi)/(lamda) xx delta`
(ii) For constructive interference, the phase difference should be, `phi = 0, 2pi , 4pi ...` Hence, the path difference must be, ` delta = 0, lamda, 2lamda....` In general, the integral multiples of `lamda`
` delta = nlamda` where, n = 0, 1, 2, 3....
(iii) For destructive interference, phase difference should be, `phi = pi ,3pi , 5pi`... Hence, the path difference must be, ` delta = lamda/2 , (3lamda)/(2)` In general, the half integral multiples of `lamda`.
` delta = (2n - 1) lamda/2 ` where, n = 1, 2, 3...