Cauchy dispersion formula

  1. 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 ?
     
    Last edited: Feb 18, 2013
  2. jcsd
  3. jtbell

    Staff: Mentor

    I think you mean to convert B's units from m2 to (μm)2. For that, you have to multiply by 10000002, not 1000000.
     
  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
     
  5. By example, I should have :

    eta = 1.72 + (0.013 / 1000000²) / 0.500²
     
  6. jtbell

    Staff: Mentor

    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?
     
    Last edited: Feb 18, 2013
  7. 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
     
  8. jtbell

    Staff: Mentor

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