Propagation of uncertainty from wavenumber to wavelength

[jbar18]

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

 

[DrClaude]

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?

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

You can also get the same desult from a simple derivative:
$$
\frac{d \lambda}{d k} = -\frac{2 \pi}{k^2} \Rightarrow \Delta \lambda = \frac{2\pi}{k^2} \Delta k
$$