Editing Fraunhofer diffraction (section)

===Diffraction by a grating===

[[File:Diffraction of laser beam by grating.jpeg|thumb|150px|Diffraction of a laser beam by a grating]] A grating is defined in Born and Wolf as "any arrangement which imposes on an incident wave a periodic variation of amplitude or phase, or both".

A grating whose elements are separated by {{math|''S''}} diffracts a normally incident beam of light into a set of beams, at angles {{math|''θ''<sub>''n''</sub>}} given by:<ref>{{Cite book | last = Longhurst | first = R. S. | title = Geometrical and Physical Optics | edition = 2nd | year = 1967 | publisher = Longmans | location = London | at = eq.(12.1)}}</ref>

<math display="block">~ \sin \theta_n = \frac{n \lambda} {S}, \quad n = 0, \pm 1, \pm 2, \ldots </math>

This is known as the [[Diffraction grating|grating equation]]. The finer the grating spacing, the greater the angular separation of the diffracted beams.

If the light is incident at an angle {{math|θ<sub>0</sub>}}, the grating equation is:
<math display="block">\sin \theta_n = \frac {n \lambda} {S} + \sin \theta_0, \quad n=0, \pm 1, \pm 2, \ldots </math>

The detailed structure of the repeating pattern determines the form of the individual diffracted beams, as well as their relative intensity while the grating spacing always determines the angles of the diffracted beams.

The image on the right shows a laser beam diffracted by a grating into {{math|''n''}} = 0, and ±1 beams.  The angles of the first order beams are about 20°; if we assume the wavelength of the laser beam is 600&nbsp;nm, we can infer that the grating spacing is about 1.8&nbsp;μm.

====Semi-quantitative explanation====

[[Image:Beugungsgitter.svg|200px|thumb|right]] A simple grating consists of a series of slits in a screen. If the light travelling at an angle {{math|θ}} from each slit has a path difference of one wavelength with respect to the adjacent slit, all these waves will add together, so that the maximum intensity of the diffracted light is obtained when:
<math display="block">W \sin \theta = n \lambda, \quad n=0, \pm 1, \pm 2, \ldots </math>

This is the same relationship that is given above.