Linewidths - Frequency and Wavelength

In summary, the conversation discusses the confusion regarding relating line width in frequency to one in wavelength. It is stated that if there is a broader spread of frequencies, there must be a broader spread of wavelengths. However, the mathematical relation between Δf and Δλ shows that if df is positive, dλ is negative. The conversation ends with reassurance to have faith in oneself and their mathematical abilities.
  • #1
Naz93
29
2
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??
 
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  • #2
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.
 

Related to Linewidths - Frequency and Wavelength

What is the relationship between linewidths, frequency, and wavelength?

The linewidth of a spectral line is directly related to both the frequency and wavelength of the light being emitted or absorbed. As the frequency of the light increases, the linewidth also increases. This means that the spectral lines become broader as the frequency of the light increases. On the other hand, as the wavelength of the light increases, the linewidth decreases. This is because longer wavelengths correspond to lower frequencies, which have narrower linewidths.

What factors affect the linewidth of a spectral line?

The linewidth of a spectral line can be affected by a variety of factors, such as the temperature and pressure of the emitting or absorbing material, the type of material, and any external influences like electric or magnetic fields. Additionally, the intrinsic properties of the emitting or absorbing particles, such as their energy levels and transition probabilities, can also affect the linewidth of a spectral line.

How is linewidth measured?

The linewidth of a spectral line is typically measured using spectroscopy techniques, such as absorption or emission spectroscopy. In these methods, the spectral line is compared to a known reference line, and the difference in frequency or wavelength is used to determine the linewidth. Other methods, such as Fourier transform spectroscopy, can also be used to measure linewidths with high precision.

Why are linewidths important in scientific research?

Linewidths play a crucial role in understanding the physical properties and behavior of matter at the atomic and molecular level. By studying the linewidths of spectral lines, scientists can gain insight into the composition, temperature, and pressure of different materials and environments. Linewidths also have practical applications, such as in the development of lasers and other optical technologies.

Can linewidths be manipulated or controlled?

Yes, linewidths can be manipulated or controlled through various methods. For example, by changing the temperature or pressure of the emitting or absorbing material, the linewidth of a spectral line can be altered. Additionally, external influences like electric or magnetic fields can also affect the linewidth. Scientists are also researching ways to actively manipulate linewidths using techniques such as laser cooling and precision control of atomic and molecular interactions.

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