Changes

Of course, thickness is not the only thing we need. After calculating <math> \tau </math> and uncovering the mirror, we will also detect the third laser reflection. We can calculate that the amplitude of this new combined wave will be

Of course, thickness is not the only thing we need. After calculating <math> \tau </math> and uncovering the mirror, we will also detect the third laser reflection. We can calculate that the amplitude of this new combined wave will be

<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) + 2 C _1 \cos ( - d _1 ) + 2 C _2 \cos ( - d _2 ) </math>

<math>A^2 _{123} = 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 _1 A^2 \cos ( - d _1 ) + 2 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

Simplifying our initial equation, we find that  

Simplifying our initial equation, we find that  

<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) + 2 C _1 \cos ( - 2 s / v _a ) + 2 C _2 \cos ( - 2 \tau / v _d - 2 s / v _a ) </math>

<math>A^2 _{123} / A^2 =  1 + C^2 _1 + C^2 _2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) + 2 C _1 \cos ( - 2 s / v _a ) + 2 C _2 \cos ( - 2 \tau / v _d - 2 s / v _a ) </math>

Because the cosine is an even function, we can slightly simplify this further.

Because the cosine is an even function, we can slightly simplify this further.

<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) + 2 C _1 \cos ( 2 s / v _a ) + 2 C _2 \cos ( 2 \tau / v _d + 2 s / v _a ) </math>

<math>A^2 _{123} / A^2 = 1 + C^2 _1 + C^2 _2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) + 2 C _1 \cos ( 2 s / v _a ) + 2 C _2 \cos ( 2 \tau / v _d + 2 s / v _a ) </math>

This equation, athough complicated, is completely solvable, as the only unknown is the s-term.

This equation, athough complicated, is completely solvable, as the only unknown is the s-term.