Editing Wave interference (section)

=== Between two plane waves ===
[[File:interference of plane waves 3.svg|class=skin-invert-image|thumb|Geometrical arrangement for two plane wave interference]] 
[[File:Interferences plane waves.jpg|thumb|Interference fringes in overlapping plane waves]]
A simple form of interference pattern is obtained if two [[plane wave]]s 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

<math display="block"> \Delta \varphi = \frac {2 \pi d} {\lambda} = \frac {2 \pi x \sin \theta} {\lambda}.</math>

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

<math display="block"> \frac {x \sin \theta} {\lambda} = 0, \pm 1, \pm 2, \ldots ,</math>

and are half a cycle out of phase when

<math display="block"> \frac {x \sin \theta} {\lambda} = \pm \frac {1}{2}, \pm \frac {3}{2}, \ldots </math>

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

<math display="block"> d_f = \frac {\lambda} {\sin \theta}</math>

and {{math|''d<sub>f</sub>''}} is known as the fringe spacing.  The fringe spacing increases with increase in [[wavelength]], and with decreasing angle {{math|θ}}.

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