A certain helium-neon laser emits red light in a narrow band...

Name: Problem 1, Chapter 33: Fundamentals of Physics
Uploaded: 2021-07-07T14:48:54-08:00
Duration: 1 min 46 s
Channel: Sheh Lit Chang
Description: A certain helium-neon laser emits red light in a narrow band of wavelengths centered at 632.8 nm and with a "wavelength width" (such as on the scale of Fig. 33-1 ) of 0.0100 nm. What is the corresponding "frequency width" for the emission?

A certain helium-neon laser emits red light in a narrow band of wavelengths centered at $632.8 \mathrm{nm}$ and with a "wavelength width" (such as on the scale of Fig. $33-1$ ) of $0.0100 \mathrm{nm}$. What is the corresponding "frequency width" for the emission?

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Key Concepts

Differential Relation and Error Propagation

When dealing with small changes or uncertainties in wavelength, it is useful to apply differential calculus to propagate these changes to the frequency domain. By differentiating the relation c = ??, one obtains d?/d? = -c/?², which approximates the change in frequency (??) related to a small change in wavelength (??) as ?? ? (c/?²)??. This concept of error propagation in non-linear relationships is crucial when converting between measurement uncertainties in wavelength and frequency.

Electromagnetic Wave Relationship

Electromagnetic waves are characterized by the relationship c = ??, where c is the speed of light, ? is the wavelength, and ? is the frequency. This fundamental relation establishes that wavelength and frequency are inversely related, meaning that a change in wavelength corresponds to a change in frequency. It is therefore central to understanding how narrow spectral lines in lasers translate between the two domains.

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