Changes

== Ideal Amplitude Calculation ==

== Ideal Amplitude Calculation ==

[[Image:03 Apparatus for Beam 00.png|thumb|The zeroth wave.]]

[[Image:03 Apparatus for Beam 00.png|thumb|The zeroth wave path. Although some light passes through the splitter, it is lost, cannot affect the experiment, and therefore is not illustrated.]]

Because all three waves are reflections of the same original wave, they all have the same wavelength. However, the processes of reflection and transmission will modify the ''amplitude'' of each wave. By removing the diamond and reflecting the laser solely off of the mirror, we will be able to calculate the amplitude of the initial light after it has reflected off the mirror and beam splitter once and been transmitted through the splitter once.  

Because all three waves are reflections of the same original wave, they all have the same wavelength. However, the processes of reflection and transmission will modify the ''amplitude'' of each wave. By removing the diamond and reflecting the laser solely off of the mirror, we will be able to calculate the amplitude of the initial light after it has reflected off the mirror and beam splitter once and been transmitted through the splitter once.  

== Ideal Thickness Calculation ==

== Ideal Thickness Calculation ==

[[Image:04 Appa for Beam 01.png|thumb|The first wave reflection.]]

[[Image:04 Appa for Beam 01.png|thumb|The first wave path. Although some light reflects off the splitter, it is lost, cannot affect the experiment, and therefore is not illustrated.]]

To find the thickness of the diamond, we ideally only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply remove the mirror.

To find the thickness of the diamond, we ideally only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply remove the mirror.

<math>A^2 _{012} = C^2 _0 A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 A^2 \cos ( d _2 - d _1 ) + 2 C _0 C _1 A^2 \cos ( - d _1 ) + 2 C _0 C _2 A^2 \cos ( - d _2 ) </math>

<math>A^2 _{012} = C^2 _0 A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 A^2 \cos ( d _2 - d _1 ) + 2 C _0 C _1 A^2 \cos ( - d _1 ) + 2 C _0 C _2 A^2 \cos ( - d _2 ) </math>

Although this equation looks very complicated, we know that

Although this equation looks very complicated, we know that

== Compensating for Internal Reflection ==

== Compensating for Internal Reflection ==

[[Image:02 Internal Reflection with Labels.png|thumb|Internal reflection, where C is a coefficient to be multiplied by the amplitude. The angles have been exaggerated from zero degrees.]]

[[Image:02 Internal Reflection with Labels.png|thumb|Internal reflection of the diamond, where C is a coefficient to be multiplied by the incoming amplitude. The angles have been exaggerated from zero degrees. The diagram also shows that all error comes from about two percent of the amplitude.]]

Realistically, the laser will not miraculously split in two upon reaching the diamond, creating one wave that reflects back and a second that reflects off of the back of the diamond and then passes perfectly through the front. Internal reflection will occur; we must calculate how much there will be and whether or not we must compensate for it.

Realistically, the laser will not miraculously split in two upon reaching the diamond, creating one wave that reflects back and a second that reflects off of the back of the diamond and then passes perfectly through the front. Internal reflection will occur; we must calculate how much there will be and whether or not we must compensate for it.