Changes

This tells us that about 83% of the laser will be transmitted through the diamond at each reflection. This tells us <math> C _1 </math>:

This tells us that about 83% of the laser will be transmitted through the diamond at each reflection. This tells us <math> C _1 </math>:

<math> C _1 = 0.17189 </math>

<math> C _1 = R = 0.17189 </math>

For <math> C _2 </math>, we must take into account two transmissions and one reflection. The calculation is easy:

For <math> C _2 </math>, we must take into account two transmissions and one reflection. The calculation is easy:

<math> C _2 = 0.117876 </math>

<math> C _2 = R T^2 = 0.117876 </math>

We can continue and calculate <math> C _3</math>, <math> C _4</math>, and <math> C _5</math>.

We can continue and calculate <math> C _3</math>, <math> C _4</math>, and <math> C _5</math>.

<math> C _3 = 0.003483 </math>

<math> C _3 = R^3 T^2 = 0.003483 </math>

<math> C _4 = 0.000103 </math>

<math> C _4 = R^5 T^2 = 0.000103 </math>

<math> C _5 = 0.000003 </math>

<math> C _5 = R^7 T^2 = 0.000003 </math>

Using just these five waves, we can recalculate our shape term.

Using just these five waves to begin with, we can recalculate our shape term.

<math>\frac{A^2 _{12345}}{A ^2} = C^2 _1 + C^2 _2  + C^2 _3 + C^2 _4 + C^2 _5 + 2 C _1 C _2 \cos ( d _2 - d _1 ) + 2 C _1 C _3 \cos ( d _3 - d _1 ) + 2 C _1 C _4 \cos ( d _4 - d _1 )</math>

<math>\frac{A^2 _{12345}}{A ^2} = C^2 _1 + C^2 _2  + C^2 _3 + C^2 _4 + C^2 _5 + 2 C _1 C _2 \cos ( d _2 - d _1 ) + 2 C _1 C _3 \cos ( d _3 - d _1 ) + 2 C _1 C _4 \cos ( d _4 - d _1 )</math>

<math> + 2 C _3 C _5 \cos ( d _5 - d _3 )+ 2 C _4 C _5 \cos ( d _5 - d _4 ) </math>

<math> + 2 C _3 C _5 \cos ( d _5 - d _3 )+ 2 C _4 C _5 \cos ( d _5 - d _4 ) </math>

This is an unnerving equation. However, we only have eleven terms that need to be calculated. We can begin with the sum of C-terms and compare it to the idealized version.

This is an unnerving equation. However, we only have eleven C-terms that need to be calculated. We can begin with the sum of C-terms and compare it to the idealized version.

<math> C^2 _1 + C^2 _2  + C^2 _3 + C^2 _4 + C^2 _5 = 0.043453</math>

<math> C^2 _1 + C^2 _2  + C^2 _3 + C^2 _4 + C^2 _5 = 0.043453</math>

Once again, the terms become very small very quickly. Because even the largest internal-reflection induced term (<math> 2 C _2 C _3 </math>) is more than an order of magnitude smaller than the needed terms, we can treat all internal reflection as error and ignore it.

Once again, the terms become very small very quickly. Because even the largest internal-reflection induced term (<math> 2 C _2 C _3 </math>) is more than an order of magnitude smaller than the needed terms, we can treat all internal reflection as error and ignore it.

This rapid decrease in amplitude is primarily because much of the initial amplitude is completely lost during the reflection process, since 83% of any remaining amplitude is lost each time the wave reflects off of the back of the diamond. This decrease is ''very'' significant. For example, when the wave <math> \Psi _2 </math> exits the diamond, the light reflected back into the diamond has an amplitude less than three percent of the original wave, and 83% of ''this'' is lost when the wave reflects off of the back of the diamond, leaving less than half a percent of the initial amplitude.

This rapid decrease in amplitude is primarily because much of the initial amplitude is completely lost during the reflection process, since 83% of any remaining amplitude is lost each time the wave reflects off of the back of the diamond. This decrease is ''very'' significant. For example, when the wave <math> \Psi _2 </math> exits the diamond, the light reflected back into the diamond has an amplitude less than three percent of the original wave, and 83% of ''this'' is lost when the wave reflects off of the back of the diamond, leaving less than half a percent of the initial amplitude to make up all errors.

== Color of the Laser ==

== Color of the Laser ==