Diffraction

Diffraction is a phenomenon that describes the apparent bending and spreading of waves when they meet an obstruction. Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser.

One of the most well-known forms of diffraction is single-slit diffraction, which occurs when waves pass through a narrow gap. The waves bend and spread from the gap, and if coherent, may cause a pattern of interference beyond the gap (known as a diffraction pattern). Diffraction depends on the size of the gap compared to the wavelength of the waves involved; the greatest effects are observed when the gap equals the wavelength.

From monochromatic waves of wavelength λ incident on a slit of width d, the intensity I of the diffracted waves at an angle θ is given by:

I(θ) = [ sinc( {πd / λ} sin θ ) ]² ,

where sinc function is given by sinc(x) = sin(x)/x. If there are two or more slits through which the waves pass, a more complex diffraction pattern occurs which is the result of the coherent superposition of the diffraction patterns from each slit. A two-slit experiment is described in Young's Double-slit experiment.

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Light does not have to pass through an aperture to diffract; a beam of light of a finite size also undergoes diffraction and spreads in diameter. This affect limits the minimum size d of spot of light formed at the focus of a lens:

d = 2.44 λ f / D ,

where λ is the wavelength of the light, f is the focal length of the lens, and D is the diameter of the lens. (See Rayleigh criterion).

Diffraction also occurs when waves are scattered from a periodic structure, such as atoms in a crystal or rulings on a diffraction grating. Each scattering center (e.g., each atom) acts as a point source of spherical wavefronts; these wavefronts undergo constructive interference to form a number of diffracted beams. The direction of these beams is described by Bragg's law:

nλ = 2d sin(θ) ,

where λ is the wavelength, d is the distance between scattering centers, θ is the angle of diffraction and n is an integer known as the order of the diffracted beam. Bragg diffraction is used in X-ray crystallography to deduce the structure of a crystal from the angles at which X-rays are diffracted from it.

The most common demonstration of diffraction is the spectrum of colors seen reflected from a compact disc: the closely-spaced tracks on the surface of the disc form a diffraction grating, and the individual wavelengths of white light are diffracted at different angles from it, in accordance with Bragg's law.

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