Linewidths - Frequency and Wavelength

[Naz93]

Hi,

Probably a really stupid question... but I'm confused about how to relate a line width in frequency to one in wavelength. To me it seems obvious that if there's a broader spread of frequencies, there must be a broader spread of wavelengths, and vice versa - after all, the line is broader.

But... if you relate Δf and Δλ mathematically (f is frequency, since there was no nu on the quick symbols list):

c = fλ

f = c/λ

df/dλ = -c/(λ^2)

so df = dλ * (-c/(λ^2))

I.e. if df is positive, dλ is negative...

What am I doing wrong??

 

[sophiecentaur]

Where's the problem in that? One slope is positive and the other is negative - that's what you get when you have

λ= c/f and you write down dλ/df

No worries. Have faith in yourself and your maths.