Constructive and destructive interference can be explained in terms of phase and path difference. Interference patterns can be calculated using wavelength, grating spacing and angle of maxima.
If two waves coincide with peaks and troughs matching they are said to be in phase.
If two periodic waves of similar frequency coincide in phase the waves superimpose their wave energy to produce a wave of double the amplitude. This is constructive interference.
Destructive interference
If two waves coincide with peaks of one meeting troughts of the other they are said to be out of phase.
If two waves are exactly out of phase they will interfere destructively to produce zero amplitude.