Week of 9/11

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Revision as of 15:10, 13 September 2006

Here is a great resource for mathematics and Mathematica: Mathworld, the on-line free mathematics encyclopedia

9/13/06: More on the Fabry-Perot etalon

$E_t = (E_0 t^2) e^{i \omega L/c} + r^2 (E_0 t^2) e^{i \omega 3L/c} + r^4 (E_0 t^2) e^{i \omega 5L/c} .... \,$

or

$E_t = (E_0 t^2) e^{i \omega L/c}\left[ 1 + r^2 e^{i \omega 2L/c} + r^4 e^{i \omega 4L/c} ...\right]$

Hence

$E_t = (E_0 t^2) e^{i \omega L/c} \frac{ 1 - r^2m e^{i \omega 2mL/c}} {1 - r^2m e^{i \omega 2L/c}}$

Take the limit as the number of bounces goes to infinity, then take $| E t | 2$ and We get:

$I_t/I_i = \frac{1}{1+ K \sin^2(L \omega/c)}$

@@ Line 18: / Line 18: @@
 <math>E_t = (E_0 t^2) e^{i \omega L/c} \frac{ 1 - r^2m e^{i \omega 2mL/c}} {1 - r^2m e^{i \omega 2L/c}}</math>
+Take the limit as the number of bounces goes to infinity, then take <math>|E_t|^2</math>  and We get:
+<math>I_t/I_i = \frac{1}{1+ K \sin^2(L \omega/c)}</math>