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[Z^2 + y_1^2 ]^{1 / 2} \, .  [Z^2 + y_1^2 ]^{1 / 2} \, .  
</math>  </math>  
+  </td>  
+  </tr>  
+  </table>  
+  </div>  
+  Notice that, in the definition of <math>~D_j</math>, the expression inside the square brackets involves a term that depends quadratically on the dimensionless length scale, <math>~Y_j/L</math>, as well as a term that depends linearly on this ratio. As discussed below, our expression for the amplitude simplifies nicely in situations where the quadratic term can be ignored. Via a related simplification, we will find that the various natural lengths of this problem are can be related via the expression,  
+  <div align="center">  
+  <table border="0" cellpadding="5" align="center">  
+  
+  <tr>  
+  <td align="right">  
+  <math>~y_1\biggr_{1^\mathrm{st} \mathrm{fringe}}</math>  
+  </td>  
+  <td align="center">  
+  <math>~\approx</math>  
+  </td>  
+  <td align="left">  
+  <math>~\frac{\lambda Z}{w} \, .</math>  
</td>  </td>  
</tr>  </tr> 
Revision as of 21:47, 27 December 2017
Contents 
CGH: Philosophical Overview
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Slit Diffraction
Single Aperture

As has been detailed in an accompanying discussion, we consider, first, the amplitude (and phase) of light that is incident at a location on an image screen that is located a distance from a slit of width . The amplitude is given by the expression,



where,



and,



Notice that, in the definition of , the expression inside the square brackets involves a term that depends quadratically on the dimensionless length scale, , as well as a term that depends linearly on this ratio. As discussed below, our expression for the amplitude simplifies nicely in situations where the quadratic term can be ignored. Via a related simplification, we will find that the various natural lengths of this problem are can be related via the expression,



See Also
 Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4, pp. 8485 — Where is My Digital Holographic Display? [ PDF ]
 Diffraction (Wikipedia)
 Various Google hits:
 Single Slit Diffraction (University of Tennessee, Knoxville)
 Diffraction from a Single Slit; Young's Experiment with Finite Slits (University of New South Wales, Sydney, Australia)
 Single Slit Diffraction Pattern of Light (University of British Columbia, Canada)
 Fraunhofer Single Slit (Georgia State University)
© 2014  2021 by Joel E. Tohline 