**How to convert
cm**^{-1} to microns or nanometers
**Basics**
Spectroscopists of the *chemistry*
variety have found that inverse cm is a wonderful way to measure light. It is
proportional to the wavenumber and the frequency (and therefore energy), but it
makes those of us that are trained in rational units pull our hair out. IF you
are talking about ABSOLUTE wavelength (i.e. the wavelength of CO_{2}
laser is 10.6 microns) then the conversion goes as follows:
Wavelength in µm = 10,000/cm^{-1} So
300 cm^{-1} => 33 microns
Wavelength in nm =
10,000,000/cm^{-1}
so 20,000
cm^{-1} => 500
nm
**How to convert microns
or nm to cm**^{-1}(inverse cm)
Wavenumbers in
cm^{-1}=
10,000/µm So 10.6 microns => 943
cm^{-1}
Wavenumbers in
cm^{-1}=
10,000,000/nm So 632.8 nm => 15800
cm^{-1}
**How to convert delta
microns or nanometers to delta cm**^{-1}(inverse cm)
Of course
this is where it gets tricky, because the result depends on the absolute
wavenumber, in other words 10 cm^{-1} is 1000 microns at one
wavelength, but 0.1 microns at another. If you have a peak width of inverse
centimeters converting to a peak width of microns could be painful. But taking
the derivative of the above equations you can get the formula
d(Wavelength in µm) = (10,000 *
d(cm^{-1})/(cm^{-1})^{2})
The notation is a little awkward, sorry. What this means
is that you take the peak width [d(cm^{-1})], divide it by the absolute
wavenumber of the center of the peak [(cm^{-1})] and multiply it by
10,000 to get the peak width in µm. So a peak that is centered at
943 cm^{-1} and is 12 cm^{-1} wide would be also a peak
centered at 10.6 microns and 0.13 microns wide.
d(Wavelength in nm) = (10,000,000 *
d(cm^{-1})/(cm^{-1})^{2}) So
a peak that is centered at 20492 cm-1 with a linewidth of 10 cm-1 would also be
a peak centered at 488 nm with a linewidth of 2.4 · 10^{-8} nm.
**How to convert delta
cm**^{-1} to delta micrometers or delta nanometers
d(Wavenumber in cm^{-1}) = (10,000
* d(µm)/(µm)^{2}) Or
a peak that has wavelength of 33 microns and is 0.2 microns wide would be
centered at 303 cm^{-1} and be 1.84 cm^{-1} wide
d(Wavenumber in cm^{-1}) =
(10,000,000 * d(nm)/(nm)^{2})
or a peak that has a wavelength of 1.06 nm
and a linewidth of .01 nm would be centered at 9433962 cm^{-1} with a
line width of 89000 cm^{-1} |