What units should be used for the cauchy dispersion formula?

[spectral]

Hi everybody,

I would like to use the 'cauchy dispersion formula', ie (http://en.wikipedia.org/wiki/Cauchy's_equation):[/PLAIN]

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 ?

 

[jtbell]

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.

 

[spectral]

Thanks for your answer,

But based on the formula here :http://en.wikipedia.org/wiki/Cauchy's_equation[/PLAIN]

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

 

[spectral]

By example, I should have :

eta = 1.72 + (0.013 / 1000000²) / 0.500²

 

[jtbell]

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]

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

 

[jtbell]

I have see somewhere that the C parameter has to be in m²...

I suspect that they do their calculations using λ in meters.