I'm looking at the following plot: enter image description here

The vertical lines show the upper and lower frequency bounds for each of the bands W4, W3, W2...and I'm trying to convert them to wavelengths using $\lambda=\frac{c}{\nu}$ so that I can show a similar plot, only in wavelength space, rather than frequency.

As an example, I know that $\lambda_{W4}=22\mu$m, so $f_{W4}=1.36\times10^{13}$ Hz. What I can't figure out, is the uncertainties in the graph. It's stated in the caption that the frequency bands are $\Delta log_{10}=\pm 0.05$, but I'm not sure how to find the bounds from that. Is it:

$1.36\times 10^{13} \pm log_{10}0.05 = 1.35999\times 10^{13} \rightarrow 1.3600003\times 10^{13}$


$log_{10}(1.36\times 10^{13} \pm 0.05) = 13.08 \rightarrow 13.63$ $=1.2023\times 10^{13} \rightarrow 1.3599\times 10^{13}$

or am I completely off track?


I would interpret $\Delta\log_{10}\nu=\pm 0.05$ in the following way.

$\Delta\log_{10}\nu=+ 0.05= \log_{10} \nu_{\rm upper} - \log_{10} \nu_{\rm W4}$ and $\Delta\log_{10}\nu=- 0.05= \log_{10} \nu_{\rm lower} - \log_{10} \nu_{\rm W4}$

Knowing $\nu_{\rm W4}$ you can find $\nu_{\rm upper}$ and $\nu_{\rm lower}$ and hence $\lambda_{\rm lower}$ and $\lambda_{\rm upper}$.


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