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=CGH:  Philosophical Overview=
=CGH:  Philosophical Overview=
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==Propagation of Light==
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==Slit Diffraction==
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===Single Aperture===
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<table border="0" cellpadding="10" align="right"><tr><td align="center">
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<table border="1" cellpadding="5">
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<tr>
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  <th align="center">Figure 1</th>
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</tr>
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<tr>
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  <td align="center" bgcolor="lightgreen">[[File:Aperture3.gif|350px|Chapter1Fig1]]</td>
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</tr>
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</table>
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</td></tr></table>
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As has been detailed in an [[User:Tohline/Appendix/CGH/ParallelApertures#One-Dimensional_Aperture|accompanying discussion]], we consider, first, the amplitude (and phase) of light that is incident at a location <math>~y_1</math> on an image screen that is located a distance <math>~Z</math> from a slit of width <math>~w = (Y_1 - Y_2) = 2c</math>.  The amplitude is given by the expression,
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<div align="center">
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<table border="0" cellpadding="5" align="center">
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<tr>
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  <td align="right">
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<math>~A(y_1)</math>
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  </td>
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  <td align="center">
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<math>~=</math>
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  </td>
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  <td align="left">
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<math>~\sum_j
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a_j \biggl[ \cos\biggl(\frac{2\pi D_j}{\lambda} + \phi_j \biggr) + i  \sin\biggl(\frac{2\pi D_j}{\lambda} + \phi_j \biggr) \biggr]
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\, ,
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</math>
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  </td>
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</tr>
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</table>
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</div>
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where,
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<div align="center" id="Distance">
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<table border="0" cellpadding="5" align="center">
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<tr>
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  <td align="right">
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<math>~D_j</math>
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  </td>
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  <td align="center">
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<math>~=</math>
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  </td>
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  <td align="left">
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<math>~
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L \biggl[1 - \frac{2y_1 Y_j}{L^2} + \frac{Y_j^2}{L^2} \biggr]^{1 / 2} \, ,
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</math>
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  </td>
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</tr>
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</table>
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</div>
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and,
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<div align="center">
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<table border="0" cellpadding="5" align="center">
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<tr>
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  <td align="right">
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<math>~L</math>
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  </td>
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  <td align="center">
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<math>~\equiv</math>
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  </td>
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  <td align="left">
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<math>~
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[Z^2 + y_1^2  ]^{1 / 2} \, .
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</math>
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  </td>
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</tr>
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</table>
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</div>
=See Also=
=See Also=

Revision as of 21:25, 27 December 2017

Contents

CGH: Philosophical Overview

Whitworth's (1981) Isothermal Free-Energy Surface
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Slit Diffraction

Single Aperture

Figure 1
Chapter1Fig1

As has been detailed in an accompanying discussion, we consider, first, the amplitude (and phase) of light that is incident at a location ~y_1 on an image screen that is located a distance ~Z from a slit of width ~w = (Y_1 - Y_2) = 2c. The amplitude is given by the expression,

~A(y_1)

~=

~\sum_j
a_j \biggl[ \cos\biggl(\frac{2\pi D_j}{\lambda} + \phi_j \biggr) + i   \sin\biggl(\frac{2\pi D_j}{\lambda} + \phi_j \biggr) \biggr]
\, ,

where,

~D_j

~=

~
L \biggl[1 - \frac{2y_1 Y_j}{L^2} + \frac{Y_j^2}{L^2} \biggr]^{1 / 2} \, ,

and,

~L

~\equiv

~
[Z^2 + y_1^2  ]^{1 / 2} \, .

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation

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