Converting between Wavelength and Frequency in Resonators

In summary, the conversation discusses finding the corresponding frequency linewidth given an energy level centered around λ with a linewidth of Δλ. The formula used is Δλ/λ = Δν/ν, which is based on the concept that the % error in wavelength is the same as the % error in frequency. The conversation also mentions using the relationship c = f*λ and the concept of no error in c and % errors adding when multiplying or dividing. The conversation also briefly touches on finding the separation in wavelength for a resonator with a given length and the Free Spectral Range.
  • #1
Niles
1,866
0

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.
 
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  • #2
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.
 
  • #3
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.
 

Related to Converting between Wavelength and Frequency in Resonators

What is the relationship between wavelength and frequency?

The wavelength and frequency of a wave are inversely proportional to each other. This means that as the wavelength increases, the frequency decreases, and vice versa. This relationship is described by the equation: speed of light = wavelength x frequency.

How is wavelength measured?

Wavelength is typically measured in meters (m), centimeters (cm), or nanometers (nm). In the electromagnetic spectrum, shorter wavelengths have higher frequencies and longer wavelengths have lower frequencies.

What is the unit of frequency?

The unit of frequency is Hertz (Hz), which represents the number of cycles or oscillations per second. This unit is named after the German physicist Heinrich Hertz.

How can wavelength and frequency be calculated?

To calculate wavelength, divide the speed of light (3 x 10^8 m/s) by the frequency. To calculate frequency, divide the speed of light by the wavelength. This equation is commonly written as c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency.

Why is understanding the relationship between wavelength and frequency important in science?

Understanding the relationship between wavelength and frequency is crucial in many scientific fields, including optics, astronomy, and telecommunications. It allows us to understand and manipulate different types of waves, such as light and radio waves, and how they interact with matter. This knowledge also helps us to develop technologies that use waves, such as lasers and wireless communication devices.

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