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# Questions tagged [dispersion]

Dispersion refers to the frequency dependence of the properties of a wave.

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45 views

### Speed of light in different mediums with different frequencies

As I know the speed of the light doesn't change while it travels through a vacuum. But while it travels through a prism, it shows different deviation angles to different frequencies. So ...
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### Index of refraction of a specific wavelength using Abbe number

I am stuck with a problem, maybe my understand of it is not correct. I would like to solve, given an Abbe number and some index of refraction at a known wavelength, the ior of any wavelength λ. From ...
27 views

### Dispersion relation of a medium

In a dispersive medium I have a wave equation: $$\frac{\partial^2E}{\partial z^2} + \eta \frac{\partial^4E}{\partial z^4} - \frac{1}{c^2}\frac{\partial^2E}{\partial t^2}=0.$$ How can I find the ...
38 views

### How do you pick the wavenumber at which the group velocitiy is evaluated?

The equation for group velocity is $v_g(k) = \frac{d\omega}{dk}.$ This is obviously a function of $k$ but typically the word is used as if there is a single group velocity and not a whole function. ...
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### What does the curve branch for $\omega > \omega_p$ mean for surface plasmon dispersion?

Consider a half-infinite metal (the other half is vacuum with $\varepsilon=1$). By solving Maxwell's equations and using boundary conditions at the interface, we get the dispersion:  \frac{\...
136 views

### Why don't the oscillator coherent states disperse in time?

A Gaussian wavepacket is made of a continuum of frequencies (or energies) and stretches in time due to the phenomenon of dispersion: the different plane wave components with different frequencies ...
53 views

### Time-of-flight spectroscopy and energy-time uncertainty

I am a bit confused about spectral and temporal filtering of light. I consider a single-photon source of a bandwidth of $1\,$nm at $1550$ nm. That means, that the wavelength of the emitted photons ...
338 views

### Dispersion relations in solid state physics

Could you please explain what exactly is the relevant information that is conveyed through a dispersion relation? Edit 1: Sorry about being vague. I am currently trying to understand the dispersion ...
17 views

### Number of allowed (phonon)wave vectors in a poliatomic-basis lattice?

Lets say that my crystal is of size $N=N_1N_2N_3$ , this is the typical textbook example and after that they say that the number of allowed wavevectors is N. But tbh I dont really know if they are ...
67 views

### How to find wavepacket time dependence from the $k$-wavefunction?

I am trying to code the time dependence of a gaussian wavepacket using the Fourier transform techniques. I began with constructing a wavepacket (real parts only at the moment) at $t=0$ by multiplying ...
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### What does it mean to say that glass has refractive index 1.5?

The refractive index of a material depends on the wavelength of the light incident upon it which is why dispersion happens. When we say that glass has refractive index 1.5 which wavelength do we have ...
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### Speed of electromagnetic wave [closed]

On dispersion , speed of wave is inversely proportional to its wavelength . Therefore, gamma has max speed. But then in visible light , violet has least wavelength still it has least speed in visible ...
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### Dispersion of light

I've been taking digital signal processing course. It's pretty interesting for me. One thought came to my mind while I've been practicing numerical problem on Fourier transform. So my question is ...
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### Principle of Energy Dispersive x-ray Spectroscopy

I have a question about the EDS I don't understand how the detector can differentiate the Energy of incident x-ray simultaneously. In my thought, the emitted x-ray from the sample have different ...
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### How does refractive index increase in anomalous dispersion?

Refractive index generally increases with decrease in wavelength but in anomalous dispersion it decreases with decrease in wavelength. What causes it to be like that?
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### $E=hf$ true for all implies $E=pv$ true for all?

In the answer to this question: Can I apply $E=hf$ to a particle having mass? It was stated that $E=hf$ is true for all particles. If so, doesn't this imply that $E=$momentum x velocity is true for ...
In order to calculate the dispersion relation (i.e $w(k)$) for the electrons and protons, I used the following relations: $E = ℏω$, $p = ℏk$, and I substituted them in this formula for energy: \$E = ...