Converting between Wavelength and Frequency in Resonators

[Niles]

Homework Statement

Hi

Say I have an energy level centered around λ with some linewidth Δλ, and I wish to find the corresponding frequency linewidth Δν. What I would use is the following relation

Δλ/λ = Δν/ν.

Is this correct?

Thanks in advance.


Niles.

 

[Delphi51]

Yes. It amounts to saying the % error in wavelength is the same as the % error in frequency. This is true because c = f*λ, λ = c/f. No error in c, % errors add when multiplying or dividing.

 

[Niles]

Thanks! If I have a resonator with length e.g. L=3 micron, then the resonances are separated by (the Free Spectral Range c/2L) 50 THz. If I want to find the corresponding separation in wavelength, then how would I do that? I can't use my equation in the previous post, since that is associated with an error.