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Added some maths
'''Diffraction''' occurs ''“when [[waves]] pass through small openings, around obstacles, or past sharp edges. When an opaque object is placed between a point source of [[light]] and a screen, no sharp boundary exists on the screen between a [[shadow]]ed region and an illuminated region. The illuminated region above the shadow of the object contains alternating light and dark fringes. Such a display is called a '''diffraction pattern'''.” ''<ref>Halliday, Resnik, Walker: ''Fundamentals of Physics, 8th edition. p. 1200</ref>
'''Diffraction''' occurs ''“when [[waves]] pass through small openings, around obstacles, or past sharp edges. When an opaque object is placed between a point source of [[light]] and a screen, no sharp boundary exists on the screen between a [[shadow]]ed region and an illuminated region. The illuminated region above the shadow of the object contains alternating light and dark fringes. Such a display is called a '''diffraction pattern'''.” ''<ref>Halliday, Resnik, Walker: ''Fundamentals of Physics, 8th edition. p. 1200</ref>
==Young's Double Slit Experiment==
Consider two slits a distance <math>d</math> apart and a screen a distance <math>R</math> from the slits. To find the positions of the maxima (brightest points) on the screen, the path difference from each of the slits, <math>\Delta</math> must be an [[integer]] number of wavelengths <math>n \lambda</math>. The the angle between a ray of light from one slit and the normal of that slit is <math>\theta</math>, then for constructive interference:
<math>d \sin{\theta} = n \lambda</math>
If <math>y</math> is the distance from the centre of the screen to a maxima, then <math>y= R \tan{\theta} </math>.
If we assume the screen is much further away than the slits, such that <math>R>>d</math> then using the small angle approximation, <math>\tan{\theta} \approx \sin{\theta}</math>, rearranging gives:
<math>y_n = \frac{nR \lambda}{d}</math>
where
:<math>y_n</math> is the distance on the screen to the n<sup>th</sup> maxima
:<math>\lambda</math> is the [[wavelength]]
For destructive interference, the path difference must be <math>(n+\frac{1}{2}) \lambda</math>. This gives:
<math>y_n = \frac{(n+ \frac{1}{2})R \lambda}{d}</math>
for the n<sup>th</sup> minima.
==References==
==References==
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