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.
Interference can arise with one source of waves where the waves travel different distances before meeting.
The difference in the distance travelled (the path difference) must be a full number of wavelengths for constructive interference.
For destructive interference the path difference must be an odd number of half wavelengths.
Only waves exhibit constructive and destructive interference in everyday experience. Sound waves and water waves show interference effects. We now also know that all electromagnetic waves demonstrate interference effects.
This was shown in the first ‘double slit’ experiment conducted by Thomas Young in 1801. Young's experiment showed interference of light. As only waves demonstrate interference, this confirmed that light was a wave motion not a stream of particles.
Watch this video for a practical demonstration of how to measure the wavelength of a laser beam, also called the double slit experiment.