structural:reformatting
Between two plane waves

A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle.One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave. Assuming that the two waves are in phase at the point B, then the relative phase changes along the x -axis. The phase difference at the point A is given by

Δ φ = 2 π d λ = 2 π x sin θ λ. {\displaystyle \Delta \varphi ={\frac {2\pi d}{\lambda }}={\frac {2\pi x\sin \theta }{\lambda }}.}

It can be seen that the two waves are in phase when

x sin θ λ = 0, ± 1, ± 2, …, {\displaystyle {\frac {x\sin \theta }{\lambda }}=0,\pm 1,\pm 2,\ldots,}

and are half a cycle out of phase when

x sin θ λ = ± 1 2, ± 3 2, … {\displaystyle {\frac {x\sin \theta }{\lambda }}=\pm {\frac {1}{2}},\pm {\frac {3}{2}},\ldots }

Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is

d f = λ sin θ {\displaystyle d_{f}={\frac {\lambda }{\sin \theta }}}

and d is known as the fringe spacing. The fringe spacing increases with increase in wavelength, and with decreasing angle θ.

The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.