# Diffraction New

student em Warwick University
24 de Mar de 2009
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### Diffraction New

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• 7. As you will notice the bright fringes in a single slit pattern are many times wider than the dark fringes. (The formula used to predict the position of the dark fringes is the same as the diffraction grating formula, except that it is used to predict minima rather than maxima, this is not specified in the spec though)
• 8. Additional notes: Huygens principle If we take situation a to be a wave before it passes through a slit, then the wave front is linear. In this model the wave front is a made up of a series of wavelets, each of which will have a point source at some point behind them. As these wavelets (and therefore their point sources) pass through a narrow opening they will diffract, to give a continuous curved wave front made up of wavelets. However as the wavelets are no longer in one line, they will start to interfere with each other despite their coherent nature.
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• 15. Derivation of n  = d sin  (Required) Consider a diffraction grating with slit spacing d . For the beam leaving a and b to form the first maxima on the screen they must be in phase  path difference of  . Distance bc must therefore be  (or n  as 1 st order). Distance ab must = d Angle b â c =  Using trig. Sin  = opp/hyp (opp = n  , hyp = d)  Sin  = n  /d (or n  = d sin  )
• 16. 2 nd order (further explanation) c The next point at which we will get a maxima is when the path difference is sufficient for the waves to be in phase. This will next happen when the path difference bc is 2  . In this case sin  = 2  /d Each successive maxima will have a path difference of n  (where n is the order of the diffraction fringe). We can predict the number of fringes to appear as the maximum value of sin  is 1, by rearranging our formula we can calculate the maximum value of n .
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