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Cauchy dispersion formula

by spectral
Tags: cauchy, dispersion, formula
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spectral
#1
Feb18-13, 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 / w

Where :
eta is the resulting IOR
A is the base IOR
B is the dispersion coefficient expressed in squarre meter (m)
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 m : 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 ?
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jtbell
#2
Feb18-13, 08:11 AM
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Quote Quote by spectral View Post
1) I convert the B parameter from micro-meter to m : 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.
spectral
#3
Feb18-13, 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 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 1000000 ?

Or there is something wrong in what I do or my units ?

Thanks

spectral
#4
Feb18-13, 08:41 AM
P: 4
Cauchy dispersion formula

By example, I should have :

eta = 1.72 + (0.013 / 1000000) / 0.500
jtbell
#5
Feb18-13, 09:25 AM
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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?
spectral
#6
Feb18-13, 09:37 AM
P: 4
I see...

It is just that I have see somewhere that the C parameter has to be in m... but it seems false !

Thanks for your help
jtbell
#7
Feb18-13, 09:52 AM
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Quote Quote by spectral View Post
I have see somewhere that the C parameter has to be in m...
I suspect that they do their calculations using λ in meters.


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