Changes

Light is a wave, and can be expressed as

Light is a wave, and can be expressed as

<math>\Psi = A \sin ( \omega t + d ) </math>

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

where A is the amplitude, <math>\omega</math> is the frequency, t is time, and d is the phase-shift.

where <math> A _{laser} </math> is the amplitude of the initial laser, <math>\omega</math> is the frequency, t is time, d is the phase-shift, and C is a constant dependent on the reflectivity of all surfaces the laser intercepts.

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} = \Psi _1 = C _1 A \sin ( \omega t + d _1 ) </math>

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

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

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

<math>\Psi _{Mirror} = \Psi _3 = C _3 A \sin ( \omega t) </math>

<math>\Psi _{Mirror} = \Psi _0 = C _0 A _{laser} \sin ( \omega t) </math>

(For simplicity, we will say that the wave leaving the mirror has not been phase-shifted, as above.)

(For simplicity, we will say that the wave leaving the mirror has not been phase-shifted, as above.)

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. However, the processes of reflection and transmission will modify the amplitudes 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. The mirror has a coefficient of reflection r = 100, so we are only concerned with that of the half-silvered mirror. The recorded amplitude will be equal to <math> C _0 A _{laser} </math>.

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.

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.

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) </math>

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \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 radians. Because this measurement is in unhelpful units, we can multiply it by the frequency <math> \gamma </math> and divide by <math> 2 \pi </math> for the thickness <math> \tau </math> in meters.

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 radians. Because this measurement is in unhelpful units, we can multiply it by the wavelength <math> \gamma </math> and divide by <math> 2 \pi </math> for the thickness <math> \tau </math> in meters.

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

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