Editing Fraunhofer diffraction (section)

====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>