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Cauchy dispersion formula 
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#1
Feb1813, 08:02 AM

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 micrometers I try to apply this formula this way : B = 0.013 in micrometers, A = 1.72 So first, 1) I convert the B parameter from micrometer to m² : B = B / 1000000 2) I convert my wavelenght from nm to micrometer : wv = 500 / 1000 But the result I got seems incorrect, I got no dispersion !!! Maybe there is a problem with my units ? 


#2
Feb1813, 08:11 AM

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P: 11,609




#3
Feb1813, 08:38 AM

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 micrometers !!!! So, if C = 0.013 in micrometers 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 


#4
Feb1813, 08:41 AM

P: 4

Cauchy dispersion formula
By example, I should have :
eta = 1.72 + (0.013 / 1000000²) / 0.500² 


#5
Feb1813, 09:25 AM

Mentor
P: 11,609

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 / λ^{2} = 0.013 / 0.5^{2} has units of (μm)^{2}/(μm)^{2}, i.e. it's unitless, as it should be because the index of refraction is unitless. Why do you want to convert B to m^{2}? 


#6
Feb1813, 09:37 AM

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 


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