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Questions tagged [dispersion]

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

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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 ...
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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 ...
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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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How to derive the group velocity in a dispersive medium and how to interpret it in momentum space? [closed]

I had this homework where I was supposed to derive the group velocity of a given wave packet $$\psi (x,t) = \frac{1}{\sqrt{2\pi}}\int_{-\infty }^{\infty}dk\,g(k)e^{i(\omega t-kx)}$$ where $$g(k)=e^{-\...
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1answer
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Why violet light bends the most? [duplicate]

I have read about refraction through a triangular prism,rainbow formation and other natural phenomena.They all told about the strong bending of violet light . I know that it has a shorter wavelength ...
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3answers
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Proof that $v=\frac{dE}{dp}$ at relativistic speeds?

This is a formula I have seen stated in two different places in a relativistic context, but I do not know the proof and seem unable to derive it on my own. $E$ is the energy of a free particle, $v$ is ...
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Why is the phase velocity of waves on a rope independent of the wave length?

A rope is described by the wave equation $$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$ It is well known that there is no dispersion for resulting wave solutions. This implies that all plane waves ...
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The effect of velocity on dispersion of light

It is stated that red light bends less than blue light as white light is dispersed through a glass prism. I understand that red light travels faster within the glass because of its higher wavelength, ...
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Treatment of electrons and phonons in condensed matter physics

I was watching the lectures by steve simon(oxford) on solid-state physics. In the course, he derived the dispersion relation for phonons(assuming spring between atoms) and dispersion relation for ...
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Why does the phase velocity of a string attached to springs depend on the wave length?

A string can be described by the wave equation $$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$ while a string attached to a spring (i.e. with a harmonic restoring force) at each location is ...
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Dispersion: any software to work out the dispersed waveforms of EMW signals that propagate via interstellar medium for some distance?

I asked this question in the Astronomy site, but seems few people feel interested in, so I hope to have a try here in the Physics site...... Is there any software (toolbox, code, package, paid or ...
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Why is group velocity the important velocity?

It seems that universally in all systems, group velocity is the relevant velocity but why? I read that this is the speed of information transmission but why is that the case? How do you define where ...
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4answers
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Sound frequencies travel at the same speed?

as the diagram shows sound frequencies travel at the same speed or each frequency has a given speed ?
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1answer
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What happens to frequency during dispersion?

I'm a bit confused about what happens to frequency during the dispersion of white light passing through a prism. I understand that when a light wave is travelling in one medium, velocity is constant ...
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Dispersion under Classical and Quantum regimes

If I understand correctly the literature on dispersion, the atom is modeled as an electron bound to an atom by a spring with the electron behaving as a driven, damped oscillator. The electron ...
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What is a dispersive and reactive medium in mechanical waves?

Would it be possible to have some explanation about the dispersive and reactive medium in the field of mechanical waves. As far as I understand : Let $\omega$ be the excitation frequency and $\...
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Wave packet - phase vs group velocity

So, I've been revising QM recently and the concept of group vs phase velocity has me confused. Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
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1answer
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Interpreting phonon dispersion relations

I have been working with phonon dispersion relations for a while now on the topic of metamaterials (phononic band gaps). However, I still do not feel that I have fully grasped how to interpret these ...
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2answers
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Why does violet light bend the most? [duplicate]

When white light passes through a prism, refraction occurs and it splits into its seven constituent colours. If the spectrum is obtained on a screen violet light appears much more bent than red light. ...
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2answers
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Do gravitational waves disperse/refract (like EM waves in a prism)?

I have read this question: What is the relationship between a gravitational wave and a graviton? where kingledion says: Gravitational waves were theorized a century ago and recently ...
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Dispersion, surface acoustic wave devices

I am trying to understand dispersion, and to do it within the context of surface acoustic waves (SAWs). For surface acoustic wave devices the inter-digital transducers (IDTs) produce Rayleigh waves ...
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3answers
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How to describe the unit vector for a complex wave vector?

In optics, we often come across complex wave vectors that describe absorption, dispersion, etc. given as: $\textbf{k} = \textbf{k}_{real} + i\textbf{k}_{imag}$ The electric field in phasor notation ...
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1answer
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Color dispersion at the edge of a slanted mirror

When I look at the edge of a slanted mirror it looks like its affected by color dispersion which you can see by Image 1 but, when it reflects off the flat part of the mirror it looks normal, Image 2. ...
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2answers
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If a black colored body absorbs all colors, why does the spectrum of light appear on a black shoe?

Few days back in a 10 grade school practical, we were shown the dispersion of light by a prism to create spectrum. Then we went into the open sun and performed it under a linear building roof and ...
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Klein-Gordon/Maxwell Equation: dissipative or dispersive?

In Aspects of Symmetry, Coleman says (p. 185) ''Most of the simple field theories with which we are familiar have the property that all of their non-singular solutions of finite total energy are ...
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Why does the intensity of the scattered light vary when a monochromatic laser is shined into a transparent object?

When a laser is shined into a glass ball such as this video (link) or a bottle of water (link) the light is refracted through the whole transparent body. However, the intensity of the light scattered ...
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Why doesn’t a normal window produce an apparent rainbow?

When light refracts in a prism it creates a rainbow. My question is, why don’t all windows or transparent objects create this dispersion, i.e. why is the refractive index dependent on frequency in a ...
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Dispersion through Glass Slab

My questions related Dispersion through Glass Slab: Why does a parallel surface makes a difference? Why is that light do get disperse in a prism and a glass slab at surface one but at backs normal ...
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Physical Interpretation of Energy-wavenumber Graphs

Consider an energy-wavenumber graph, typical in solid state physics, like the one below. I can follow the mathematics in the derivations with a KP model. But I don't understand the physical ...
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1answer
117 views

Can dispersion relations be derived using Euler-Lagrange equations?

The question is long because of the demonstrations I give, but the problem is simple, so bear with me for a minute. I am trying to derive the dispersion relation of a semi-infinite system using Euler-...
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2answers
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What does phase velocity physically represent, and why can it be superluminal? [duplicate]

Phase velocity is defined as $v_p=\frac{\omega}{k}$ and is described in various textbooks as being the speed at which the phase of a wave propagates. If you have a wave train that is modulated by an ...
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1answer
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Wave packet in dispersive medium, how will the group velocity be affected? [closed]

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
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Dispersion relations in 2 atom and above

I am having a little trouble understanding this information of dispersion relations show below for a two atom basis. So it states that there should be in total 6 dispersion branches but there only 4. ...
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Where does dispersion actually take place?

Out of 1 & 2, which is most accurate? And, out of 3 & 4, which is most accurate? Do they both agree with each other? Please explain?
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Group and phase velocity for a superposition of 2 monochromatic waves

A wave packet in one dimension with a dispersion relation $\omega$ is a function of the form: $$f(x,t):=\sum_{i=1}^n\lambda_i\exp[i(k_i x+\omega[k_i] t)]\hspace{1cm}\forall i\leq n\colon\lambda_i,k_i\...
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1answer
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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{\...
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2answers
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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 ...
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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 ...
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2answers
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 ...
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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 ...
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1answer
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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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2answers
171 views

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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1answer
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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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1answer
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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 ...
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What really is the speed of light in a medium/vacuum, group or phase velocity?

While reading about refractive index 2 terms popped up, group velocity which alway slows down in a medium and phase velocity which may exceed speed of light. Say in a complete vacuum and using laser ...
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Spring constant and dispersion relation

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 = ...