# Cauchy dispersion formula

by spectral
Tags: cauchy, dispersion, formula
 P: 4 Hi everybody, I would like to use the 'cauchy dispersion formula', ie (http://en.wikipedia.org/wiki/Cauchy's_equation): eta = A + B / w² Where : eta is the resulting IOR A is the base IOR B is the dispersion coefficient expressed in squarre meter (m²) w is wavelength expressed in micro-meters I try to apply this formula this way : B = 0.013 in micro-meters, A = 1.72 So first, 1) I convert the B parameter from micro-meter to m² : B = B / 1000000 2) I convert my wavelenght from nm to micro-meter : wv = 500 / 1000 But the result I got seems incorrect, I got no dispersion !!! Maybe there is a problem with my units ?
Mentor
P: 10,699
 Quote by spectral 1) I convert the B parameter from micro-meter to m² : B = B * 1000000
I think you mean to convert B's units from m2 to (μm)2. For that, you have to multiply by 10000002, not 1000000.
 P: 4 Thanks for your answer, But based on the formula here :http://en.wikipedia.org/wiki/Cauchy's_equation the C parameters (I use B instead) is expressed in micro-meters !!!! So, if C = 0.013 in micro-meters I have to convert it to meters to use the Cauchy formula... ... then I "divide" by 1000000² ? Or there is something wrong in what I do or my units ? Thanks
P: 4

## Cauchy dispersion formula

By example, I should have :

eta = 1.72 + (0.013 / 1000000²) / 0.500²
 Mentor P: 10,699 OK, I see now. I didn't look at the Wikipedia page to see where the numbers came from before. If your B (their C) is already in units of (μm)2, and you've converted your wavelength λ to μm, then the quantity B / λ2 = 0.013 / 0.52 has units of (μm)2/(μm)2, i.e. it's unit-less, as it should be because the index of refraction is unit-less. Why do you want to convert B to m2?
 P: 4 I see... It is just that I have see somewhere that the C parameter has to be in m²... but it seems false ! Thanks for your help
Mentor
P: 10,699
 Quote by spectral I have see somewhere that the C parameter has to be in m²...
I suspect that they do their calculations using λ in meters.

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