Changes

We have a sum of three waves, which can be expressed as

We have a sum of three waves, which can be expressed as

<math>\Psi _{Front Of Diamond} = A \sin ( \omega t + d _1 ) </math>

<math>\Psi _{Front Of Diamond} = C _1 A \sin ( \omega t + d _1 ) </math>

<math>\Psi _{Back Of Diamond} = A \sin ( \omega t + d _2 ) </math>

<math>\Psi _{Back Of Diamond} = C _2 A \sin ( \omega t + d _2 ) </math>

<math>\Psi _{Mirror} = A \sin ( \omega t) </math>

<math>\Psi _{Mirror} = A \sin ( \omega t) </math>

Because all three waves are reflections of the same original wave, they all have the same amplitude and frequency.

Because all three waves are reflections of the same original wave, they all have the same amplitude and frequency.

To find the thickness of the diamond, we only need the first two waves. Although later all three waves will be inexorably tied together, we can begin with only two.

To find the thickness of the diamond, we only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply obscure the mirror with something that absorbs light, like a black cloth.

The combined wave equation is unimportant, since we only record its amplitude, which is

The combined wave equation is unimportant, since we only record its amplitude, which is

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

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

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

 

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

 

 

<math>A^2 _{total} = 2 A^2 (1 + \cos ( d _2 - d _1 ) ) </math>

Because the wave reflecting off the back of the diamond travels through the diamond twice, the term <math> d _2 - d _1 </math> is twice the thickness of the diamond, in seconds. Because this measurement is in unhelpful units, we can multiply it by the speed of light in a diamond and divide by two for the thickness <math> \tau </math>.

Because the wave reflecting off the back of the diamond travels through the diamond twice, the term <math> d _2 - d _1 </math> is twice the thickness of the diamond, in seconds. Because this measurement is in unhelpful units, we can multiply it by the speed of light in a diamond and divide by two for the thickness <math> \tau </math>.

<math> ( d _2 - d _1 ) V / 2 = \tau </math>

<math> ( d _2 - d _1 ) V / 2 = \tau </math>

== Calculating the Shape ==

== Calculating the Shape ==