Editing Fraunhofer diffraction (section)

===Diffraction by a double slit===
[[File:SodiumD two double slits 2.jpg|thumb|200px|Double-slit fringes with sodium light illumination]]
In the [[double-slit experiment]], the two slits are illuminated by a single light beam.  If the width of the slits is small enough (less than the wavelength of the light), the slits diffract the light into cylindrical waves. These two cylindrical wavefronts are superimposed, and the amplitude, and therefore the intensity, at any point in the combined wavefronts depends on both the magnitude and the phase of the two wavefronts.<ref>{{harvnb|Born|Wolf|1999|loc=Figure 7.4}}</ref> These fringes are often known as [[Young's interference experiment|Young's fringes]].

The angular spacing of the fringes is given by
<math display="block">\theta_\text{f} = \lambda/d.</math>

The spacing of the fringes at a distance {{mvar|z}} from the slits is given by<ref>{{harvnb|Hecht|2002|loc=eq. (9.30).}}</ref>
<math display="block">w_\text{f} = z \theta_f = z \lambda/d,</math>
where {{mvar|d}} is the separation of the slits.

The fringes in the picture were obtained using the yellow light from a sodium light (wavelength = 589&nbsp;nm), with slits separated by 0.25&nbsp;mm, and projected directly onto the image plane of a digital camera.

Double-slit interference fringes can be observed by cutting two slits in a piece of card, illuminating with a laser pointer, and observing the diffracted light at a distance of 1&nbsp;m.  If the slit separation is 0.5&nbsp;mm, and the wavelength of the laser is 600&nbsp;nm, then the spacing of the fringes viewed at a distance of 1&nbsp;m would be 1.2&nbsp;mm.

====Semi-quantitative explanation of double-slit fringes====

[[Image:Double slit.svg|thumbnail|right|300px|Geometry for far-field fringes]]
The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves.

If the viewing distance is large compared with the separation of the slits (the [[far field]]), the phase difference can be found using the geometry shown in the figure.  The path difference between two waves travelling at an angle {{mvar|θ}} is given by
<math display="block">d \sin \theta \approx d \theta.</math>

When the two waves are in phase, i.e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximal, and when they are in anti-phase, i.e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel, and the summed intensity is zero.  This effect is known as [[Interference (optics)|interference]].

The interference fringe maxima occur at angles
<math display="block">d \theta_n = n \lambda,\quad n = 0, \pm 1, \pm 2, \ldots</math>
where {{mvar|λ}} is the [[wavelength]] of the light. The angular spacing of the fringes is given by
<math display="block">\theta_\text{f} \approx \lambda/d.</math>

When the distance between the slits and the viewing plane is {{math|''z''}}, the spacing of the fringes is equal to {{math|''zθ''}} and is the same as above:
<math display="block">w = z\lambda / d.</math>