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Cauchy dispersion formula

  1. Feb 18, 2013 #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. Feb 18, 2013 #2

    jtbell

    User Avatar

    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. Feb 18, 2013 #3
    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. Feb 18, 2013 #4
    By example, I should have :

    eta = 1.72 + (0.013 / 1000000²) / 0.500²
     
  6. Feb 18, 2013 #5

    jtbell

    User Avatar

    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. Feb 18, 2013 #6
    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. Feb 18, 2013 #7

    jtbell

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    Staff: Mentor

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