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Interference (wave propagation)

Two point interference in a ripple tank.

In physics, interference is the phenomenon in which two waves superpose each other to form a resultant wave of greater or lower amplitude. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.
The term interference has a different meaning in radio communications.

Contents [hide] 1 Interference 2 Constructive and destructive interference 3 Examples 4 Optical interferometry 5 General quantum interference 6 See also 7 References 8 External links

Interference

Animation: interference of waves from 2 point sources. Crests blue, troughs red/yellow.

For two coherent sources, the spatial separation between sources is half the wavelength times the number of nodal lines. The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant crest wave amplitude is increased; similarly troughs make a trough of increased amplitude. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased.
This form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different lengths. Two or more sources can only be used to produce interference when there is a fixed phase relation between them, but in this case the interference generated is the same as with a single source; see Huygens' principle.

Interference of two circular waves. Absolute value snapshots of the (real-valued, scalar) wave field. Wavelength increasing from top to bottom, distance between wave centers increasing from left to right. The dark regions indicate destructive interference.

The colors seen in a soap bubble or an oil film on water are a common example of interference. Light reflecting off the front and back surfaces of the thin soap film interferes, resulting in different colors being enhanced.

Light from any source can be used to obtain interference patterns, for example, Newton's rings can be produced with sunlight and the colours which can be seen when sunlight is reflected in a soap-bubble are white light fringes.

Constructive and destructive interference

Consider two waves that are in phase, sharing the same frequency and with amplitudes A₁ and A₂. Their troughs and peaks line up and the resultant wave will have amplitude A = A₁ + A₂. This is known as constructive interference.
If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another waves' troughs and so will tend to cancel itself out. The resultant amplitude is A = |A₁ − A₂|. If A₁ = A₂, the resultant amplitude will be zero. This is known as destructive interference.
When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.

combined waveform
wave 1
wave 2
	Two sinusoidal waves in phase	Two sinusoidal waves 180° out of phase

Examples

A conceptually simple case of interference is a small (compared to wavelength) source – say, a small array of regularly spaced small sources (see diffraction grating).
Consider the case of a flat boundary (say, between two media with different densities or simply a flat mirror), onto which the plane wave is incident at some angle. In this case of continuous distribution of sources, constructive interference will only be in specular direction – the direction at which angle with the normal is exactly the same as the angle of incidence. Thus, this results in the law of reflection which is simply the result of constructive interference of a plane wave on a plane surface.

Optical interferometry

Main article: Interference (optics)

Interference pattern produced with a Michelson interferometer.

Optical interferometry had played a major role in the advancement of physics, e.g. Young's slits interferometer and the Michelson-Morley experiment. It is also widely used in a range of physical and engineering measurement applications.