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Propagation of uncertainty from wavenumber to wavelength

  1. Mar 13, 2014 #1
    Hi,

    This is just a quick question. If wavenumber is a variable with some standard deviation Δk, how do I propagate this spread when converting from wavenumber to wavelength? Is it just 2π/Δk or is it more complex than that?

    Thanks
     
  2. jcsd
  3. Mar 13, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Its more complex than that! Think about it: with what you wrote, the worse your wavenumber measuring instrument, the better your knowledge of the wavelength?

    Check out:
    http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html#muldiv [Broken]

    You can also get the same desult from a simple derivative:
    $$
    \frac{d \lambda}{d k} = -\frac{2 \pi}{k^2} \Rightarrow \Delta \lambda = \frac{2\pi}{k^2} \Delta k
    $$
     
    Last edited by a moderator: May 6, 2017
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