# Diffraction

The diffraction is the behavior of the Onde S when they meet an obstacle which is not completely transparent for them; the phenomenon can be interpreted by the diffusion of a wave by the points of the object. Diffraction appears by the fact that after the meeting of an object, the density of the wave is not preserved according to the laws of the geometrical Optique.

Diffraction is the result of the Interférence waves diffused by each point.

Diffraction is observed with the Lumière, but also with the its, the Vague S, the Neutron S, the X-rays (an electromagnetic wave like the light) or the matter. It is a signature of the undulatory nature of a phenomenon.

To be highlighted clearly, the obstacle which the wave meets must have a relatively small characteristic size compared to the distance at which the observer is placed. If the observer is close to the object, it will observe the geometrical image of the object: that which usually appears to us. The diffraction of the matter particles, i.e. the observation of the matter particles projected against an object, makes it possible to prove that the particles also behave like waves (see the article Dualité wave-particle ).

The larger the length of a wave is compared to an obstacle, plus this wave will have of facility to circumvent, to wrap the obstacle. Thus the long waves (hectometric and kilometric wavelengths) can penetrate in the least recess of terrestrial surface while the retransmissions of satellite television are not possible that if the reception antenna “sees” the satellite.

Concerning the calculative approach, two methods can be used. Firstly, one can consider that each elementary surface of the object emits a spherical wave proportional to this surface (Principe of Huygens-Fresnel), and one summons (or one integrates) the contribution of each surface. Secondly, to explain the figure of diffraction completely, one uses the Théorie of Kirchhoff.

The concept of interference becomes all its extensive when the object has a periodic structure (network). In this case, the object can be represented like a repeated basic cell with regular intervals. The result of the wave is then the superposition - the interference - waves diffracted by the various cells (the unit cell being itself made up of points which diffuse each one the wave). It is this phenomenon which causes the irisation by a CD-ROM.

In the approach of the phenomenon, there are thus two levels of interference: the unit cell (diffraction by only one cell), and between the cells (diffraction of the complete object).

If one considers diffraction by a thin layer, one has a reflection of the light to the two interfaces of the layer. The figure of interference obtained (for example, irisations of a thin oil film) results from the interference of the waves diffused by the two interfaces.

## History

From a historical point of view diffraction was discovered with the light in 1665 by Grimaldi. She was interpreted correctly like an undulatory behavior by Huygens, then studied by Fresnel and Fraunhoffer following the experiments of Young (Trous of Young).

For historical reasons, one still distinguishes diffraction from the interferences whereas it is not necessary to do it: these two behaviors derive from the undulatory nature of a phenomenon and do not go one without the other. The reciprocal one is not true, there are interferences without diffraction in the case of the interferences by division of amplitude: gap of air, newton's rings, Perot-Fabry…

## Theoretical approach

The origin of diffraction is the undulatory nature of the phenomenon and to approach it is thus necessary in theory to go back to the equation of wave. One can show that a good approximation of the solution of a problem of diffraction is given by the Principe of Huygens-Fresnel under certain quite precise conditions (paraxial approximation, i.e. observation at relatively long distance compared to dimensions of the obstacle). This principle is founded on the idea that one can regard each point of a wave front as a secondary source and that the wave observed a little further is the result of the interferences between these point sources. Such a vision of the things is made possible thanks to the linearity of the equation of wave.

The Optique of Fourier is the field which treats undulatory behavior of the light through a system of lenses and openings in the paraxial approximation. To simplify calculations, one often uses the concept of Produit convolution.

See the detailed article Theory of diffraction.

## Examples of phenomena of diffraction

Example typical in mechanics of the fluids:

• Vague penetrating in a port by circumventing a pier

Typical examples in acoustics:

• horns of vertically lengthened alarms (the diffusion of the sound allows horizontally)
• the almost closed doors lets nevertheless pass a sound high level: diffraction by entrebâillement

Typical examples in optics:

Typical examples in Crystallography:

## See too

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