Question

What is the necessary condition on the path length difference between 2 waves that interfere

(a) constructively

(b) destructively

Answer 1

(a) Two waves interfere constructively if their path difference is zero, or an integral multiple of the wavelength, according to $\delta=nλ$ , with $n=0,1,2,3,......$

(b) Two waves interfere destructively if their path difference is a half wavelength, or an odd multiple of  

$\dfrac{\lambda}{2}$ , described by

        $\delta=(n+\dfrac{1}{2})\lambda,\text{ with } n=0,1,2,3,.......$