What is the name of the phenomenon where light waves add or cancel?

The phenomenon where light waves add or cancel is called interference.

Interference results from superposition: when waves overlap, their amplitudes combine according to their relative phase. Waves that arrive in phase reinforce one another through constructive interference, while waves that arrive out of phase reduce or cancel one another through destructive interference.

Thomas Young used interference ideas in optics around 1800, and his double-slit experiment became a famous demonstration. Light passing through two narrow slits forms alternating bright and dark bands on a screen. The bright bands come from constructive interference; the dark bands arise where the path difference produces destructive interference.

Interference is not the same as diffraction, although the two are closely related. Diffraction describes spreading and bending around openings or obstacles, while interference describes the resulting combination of overlapping waves. Interference also appears in anti-reflective coatings, laser speckle, interferometers and radio astronomy. For clear classical interference fringes, the waves generally need a stable phase relationship and compatible polarization.