The “color” of light is generally identified by the distribution of power or intensity as a function of wavelength λ. For example, visible light has a wavelength that ranges from about 400 nm to just over 700 nm. However, sometimes it is convenient to describe light in terms of units called “wavenumbers,” where the wavenumber w is typically measured in units of cm-1 (“inverse centimeters”) and is simply equal to the inverse of the wavelength:
In applications like Raman spectroscopy, often both wavelength and wavenumber units are used together, leading to potential confusion. For example, laser lines are generally identified by wavelength, but the separation of a particular Raman line from the laser line is generally given by a “wavenumber shift” Δw, since this quantity is fixed by the molecular properties of the material and independent of which laser wavelength is used to excite the line.
When speaking of a “shift” from a first known wavelength λ1 to a second known wavelength λ2, the resulting wavelength shift Δλ is given by
whereas the resulting wavenumber shift Δw is given by
When speaking of a known wavenumber shift Δw from a first known wavelength λ1, the resulting second wavelength λ2 is given by
Note that when the final wavelength λ2 is longer than the initial wavelength λ1, which corresponds to a “red shift,” in the above equations Δw < 0, consistent with a shift toward smaller values of w. However, when the final wavelength λ2 is shorter than the initial wavelength λ1, which corresponds to a “blue shift,” Δw > 0, consistent with a shift toward larger values of w.
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