Questions tagged [dispersion]

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

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Does recombination of light in a glass slab happens in the same way like in Newton's inverted prism experiment?

I know that refraction is due to different speeds of different wavelengths of light. So, How can those colors recombine to form a beam of white light (since different colors have different speeds)? ...
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Dispersion, refractive index against frequency graph

From Hecht optics page 74, the plot of $n$ , the refractive index, against $\omega$ , the angular frequency of the incoming wave is And the relation between $n$ and $\omega$ is: Where each $\omega_{...
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Propagation of electromagnetic waves through dielectric with dispersion

My question is rather simple. Imagine a dielectric with dispersion such that $\frac{ε(ω)}{ε_0} = 1+ \frac{ω_p^2}{ω^2}$ and $\frac{μ(ω)}{μ_0}= 1 + \frac{Fω^2}{ω_0^2 - ω^2}$ $ω_0<ω_p$ and $F<...
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Link between properties of dispersive systems and group velocity larger than phase velocity

I recently bumped into systems where the group velocity is larger than the phase velocity (capillary waves for example). What does it mean in terms of system properties ? When does a system have a ...
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4answers
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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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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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What is the significance of dispersion relation i.e. frequency vs. wave vector relation?

There are lots of pages in my textbook dedicated to this sole relation and frequency vs. wave vector graph. I do not understand what are practical significance and uses of the relation and the graph. ...
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1answer
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Physical meaning of third derivative with respect to position

I currently on a numerical solver for the KdV equation which reads $$ u_t + uu_x = u_{xxx} $$ I was wondering the physical sense of this third derivative with respect to $x$. I know that the $uu_x$ ...
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Differentiating Plasma Wave Modes Using Phase Difference

Graphically, the four plasma wave modes for 'cold' plasma overlap for various frequencies. According to Fundamentals of Plasma Physics by Bittencourt, the dispersion relations characterize an $\omega$-...
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Light beam vs sound beam

Why is it that it's very common to have beams of light but not beams of sound? Laser beams are widely available, and I am aware that it is also possible to direct sound, however, we rarely see ...
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Which of the following phenomena are responsible for rainbows?

Which of the following phenomena of light are responsible for the formation of a rainbow? 1) reflection, refraction, dispersion 2) refraction, dispersion, total internal reflection 3) ...
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1answer
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Are there optical materials with larger mean deviation with little to zero angular dispersion?

The following statement is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Dispersion and Spectra", page 434, topic "Dispersive Power": The mean deviation depends on the average ...
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1answer
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Is the equation for dispersive power applicable for all dispersive elements?

The following text is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Dispersion and Spectra", page 434, topic "Dispersive Power": The dispersive power of a material is defined as the ...
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How does a pure and an impure spectrum look like in optics?

The following text is from Concepts of Physics by Dr. H.C.Verma, from the chapter "Dispersion and Spectra", page 436, topic "Spectrum", sub topic "Pure and Impure Spectrum": [...] In an ideal ...
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Time delay of a laser pulse due to 2nd, 3rd and 4th order dispersions

I'll explain my problem : Given a Gaussian pulse with central wavelength 550 nm and a HMFW of 300 nm, and let's assume the pulse is transform-limited. I need to get the pulse through 1mm of quartz. ...
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Is the composition of two plane waves also a plane wave?

I'm really interesting to know more about Plasma physics for waves , it comes in my mind to ask this question related to dispertion relation topic exactly plane waves , It is well known that the plane ...
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what is the different between dispersion and wave propagation?

can I talk about wave propagation as dispersion? and what is the relationship between them? I am asking that because when I was searching about the telegraph equation (that represents the current ...
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1answer
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Why does the refractive index depend on wavelength? [duplicate]

Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the ...
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1answer
196 views

Speed of different em radiation in a medium [duplicate]

Does all frequency of light travel with the same speed in a particular material like glass? Since by cauchy's relation refractive index change with wavelength which implies the speed also changes. ...
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Do colors differ in terms of speed? [duplicate]

Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is ...
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2answers
46 views

Why does the concept of effective mass fail for linear dispersion relations?

I had a discussion about graphene and stumbled about a conceptual problem of myself about the effective mass of electrons close to the Dirac point in graphene or for any linear dispersion relation in ...
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4answers
274 views

Is light dispersed over distance by flat mirrors?

Hello and thank you for your time: Let's assume I have a 100 squared meter circular flat mirror placed 1 AU from the sun, and let's assume my intention is to shine light on a circular area on another ...
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149 views

Dispersion between analog and digital signal in optical fiber

We know that optical fiber is used to transmit data in digital format.As a result, there is either Intermodal or Intramodal dispersion occurring based on the fiber used for communication. If an ...
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1answer
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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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Light in fibre optic cables

Imagine a fibre optic cable stretching from London to New York (5571 km) carrying a data signal This data signal is split into two parts, red and blue light Both signals start travelling down 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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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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29 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 ...
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1answer
402 views

The effect of frequency and amplitude on the speed of sound

I don't do physics, but a sound-related question came up in a project. I've googled extensively but I still can't get a hang of the basics. The following are two related questions. Assume the source ...
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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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87 views

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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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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1answer
66 views

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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280 views

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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Understanding group velocity

Group velocity as a concept in Classical Waves confuse me. It's very easy to point out visually, like in this really helpful graphic here. Okay, it's the speed of the moving bulge, which, notably ...
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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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2answers
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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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Is $E=\hbar \omega$ correct for massive particles?

From Planck's relation we can say that the energy of a photon is $$E=h\nu=\hbar \omega \, .$$ where $\hbar \equiv h / 2\pi$. On the other hand, the energy of a free particle can be expressed as $$E=...
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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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4answers
123 views

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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2answers
74 views

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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Why do wave packets spread out over time?

Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?
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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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1answer
38 views

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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192 views

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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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
283 views

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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234 views

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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