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

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Why does my wooden door disperse light into a rainbow color spectrum?

On a clear morning, light comes through this window (viewed from the inside) It then hits the door on the opposite side (so viewing from the outside the door straight on the other side) There is ...
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Why do prisms work (why is refraction frequency dependent)?

It is well known that a prism can "split light" by separating different frequencies of light: Many sources state that the reason this happens is that the index of refraction is different for ...
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Does a man on the moon experience day?

Does a man on the moon (or any other similar body) experience daytime like we do? By daytime I mean looking upward and seeing a bright "sky," not dark space. If not, then what is the reason behind ...
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Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? ...
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What is energy in $z \neq 1 $ theories?

In a critical theory with dynamical critical exponent $z \neq 1 $, which amongst frequency, $\omega$, and dispersion, $E(\vec{k})$, may be referred to as ''energy''? I'm confused about this since in ...
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Minimal Extension of Wave Equation to Include Dispersion

Let's say you are modeling some process with the wave equation $\frac{1}{c^{2}}\frac{\partial^{2}\psi}{\partial t^{2}} = \nabla^{2}\psi$. You wish to improve your model by including dispersive ...
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Which electromagnetic radiation is faster in water, microwaves or light?

Well I've been asked this question, but I haven't been able to come with an answer yet using books and some web searches. The point is as the title says, to answer the question with the whole ...
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PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, ...
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Why does Snell's law not factor in wavelength?

If dispersion is caused due to different wavelengths bending with different angles, how is Snell's law right in generalizing it as $\sin(i) / \sin(r)$? Or am I missing something?
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319 views

Fermat principle: which index of refraction?

I am somewhat puzzled by a common formulation of the Fermat principle (light travel time), because it contains index of refraction related to phase velocity while light travel time through a slab of ...
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Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = ...
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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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More extensions of the wave equation for dispersion

The Phys.SE question Minimal Extension of Wave Equation to Include Dispersion extended the wave equation for only a very simple form of dispersion. However, what about more complex dispersion ...
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Why grating is an essential part of a monochromator?

From looking at these two images, it appears that the dispersed "rays" of the reflected light could be manipulated just as well if the reflecting mirror would be turned to a fixed angle. So why is ...
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Why don't the De Broglie dispersion relation contain a constant term?

Wikipedia says that the dispersion relation for a non-relativistic particle is: $$ \omega = \frac{\hbar k^2}{2m}. $$ But when I tried to calculate it myself, I seem to get a constant term in that ...
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Two different mediums can have equal index of refraction?

In other words: given a certain medium, is light's phase velocity unique?
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Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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Why does the speed of the Electromagnetic wave in the material depend on the frequency of the wave where as they are constant in vacuum (freespace)? [duplicate]

I am confused on why would the propagation speed of any EM waves at ANY frequency is constant in the free space (vacuum) but they seem to disperse in any other materials as the propagation speed of EM ...
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Interpretation of dispersion relation

In my research, I found that my system has the following dissipation relation: $$\omega^2=k^2+k_0^2\ , $$ where $k_0^{-1}$ is an intrinsic lengthscale of the system and the units are chosen so that ...
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What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of ...
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How to calculate the dispersion relation for a wave equation with non-constant speed of wave propagation?

Specifically, it is a one-dimensional wave equation for waves on a string with a non-constant cross-section, i. e. $$S(x)=S_1+S_2 \cos{2x}; \qquad c(x)=\sqrt{F/\rho\, S(x)}.$$ Separating the variables ...
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What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
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Frequency dependence of the speed of light in air

According to this link, the speed of light of different colors in a medium should be different. But if the refractive index of light in air is 1 then this means that the speed of light in air and ...
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Why is it possible to choose an arbitrary zero energy level when dealing with frequencies of a wave function?

This is a followup of my previous Why don't the De Broglie dispersion relation contain a constant term? question. Answerers pointed out that only differences in energy matter I can understand ...
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How to minimize the wavepacket dispersion?

This is a final exam problem. Here is what I can remember: We know that if an electron's wavefunction starts out as a narrow wavepacket, and moving in a region of constant potential, then the ...
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125 views

Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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The lineshape of a 2D photonic crystal dispersion diagram

Using simulation software (CST Studio), I calculated the dispersion of the eigenmodes of a photonic crystal, that is frequency vs wavenumber for the desired propagation direction. I wonder what kind ...
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139 views

Expectation value and Dispersion of an Operator

Suppose we have an operator $Q$ with eigenvalue $q$. Expectation value is $\langle Q \rangle$ and dispersion $D(Q) = \sqrt{\langle \left( Q - \langle Q \rangle \right)^2 \rangle} $. I want to find ...
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Light dispersion in water

Simple question: Water is clearly not disspersive if we have it, for example, in a glass of water. We don't see the rainbow through a glass of water. However drops of water disperse light in the ...
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240 views

Definition of energy

What is the definition of energy $E$ given a dispersion relation $\omega=\omega(k)$ where $k=|\vec k|$ and $\omega$ is not necessarily linearly proportional to $k$? What about momentum $\vec p$? This ...
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142 views

Density of States vs Dispersion

I have a rather naive question regarding DOS and dispersion. We showed the existence of a band gap in class for a small, periodic perturbation in class last week. When drawing this, the professor ...
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How does the color of fine dispersed metal particles change between silver and black?

Small dispersed particles of metals are often black, while a solid object of the same material would be some shade of silver. The most notable example is the use of metallic silver as the black color ...
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Dispersion relation for TE and TM waves in general anisotropic medium

I want to calculate the dispersion relation (the relation between $\bf k$ and permittivity and permeability tensors and $\omega$) for a TE and a TM wave with wave vector $\mathbf k=k_x\mathbf {\hat ...
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Third-order dispersion of glass

When working with short laser pulses, it is important to compensate the dispersion of a pulse passing through a material because it changes the pulse's shape. The effect of dispersion can be described ...
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Deriving Graphene energy dispersion in tight binding model

I'm trying to get into graphene, in detail, I try to derive the elec. energy dispersion. Sadly, I am not that familiar with condensed matter QM by now, so I got some basic questions and I hope to find ...
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What are some problems with Hugyen's wave model of light? [closed]

In terms of the different light phenomenon (reflection, diffraction, rectilinear propagation and dispersion), what are some problems with Huygen's wave model of light?
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Dispersion-less media

As far as I know, vacuum is the only dispersion free medium for electromagnetic waves. This makes me wonder if there are any other dispersion free media for these waves? (Experimentally established or ...
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What phenomenon is responsible for the evolution pattern of waves created by waterfalls?

I have been fascinated lately by the pattern of the waves created by a waterfall in my town. Specifically, the pattern shows a gradual decrease in the density of the waves as they travel away from ...
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On what refractive index of medium depends ? [duplicate]

does the refractive index of a medium depends on wavelength of light passing through it ? If yes then why ?
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Is difference in wave number always small?

Over the last few days I have been looking at a derivation of group velocity. The derivation is the one shown in this question Deriving group velocity. I have seen this derivation in many places, and ...
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Absorption of waves in a plasma

Suppose a plasma has characteristic frequency $\omega_p$. Since $$n = \sqrt{\left(1-\frac{\omega_p^2}{\omega^2}\right)} $$ For $\omega<\omega_p$, the refractive index will be imaginary - which ...
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Splitting of degenerate states due to perturbation

In band structures we see avoided crossing when we have degenerate eigenstates (caused by perturbation due to potential energy). However along some direction in first Brillouin zone, even though the ...
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Dispersion relation of silicon

In the case of dispersion relation of silicon having crystal plane orientation 111; what is the Sellmeier's equation for refractive index $n$ of silicon orientation 111 & what it's extinction ...
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Dispersion & Absorption in Optics

1) I understand light dispersion. But, I wonder what happens if I used a lens to focus it into a small point. Would it be a white point (would it reverse dispersion) or would I have a multicolored ...
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Why do dispersive waves get wider?

Consider the two waves $$y_1=Acos(\omega_1 t+k_1 x), \tag{1}$$ $$y_2=Acos(\omega_2 t+k_2 x), \tag{2}$$ where $\omega_i=k_iv(k_i)$ for $i=1,2$ so we have a dispersive medium. Then if we take their ...
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Dispersion of electrons in conductive medium

Say you have a 1'x 1'x 1' cube of conductive metal. If you placed an electrode on the center of one of the sides, and quickly turned it on and off, how would the electrons disperse? Both initially ...
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Wave Packets, Group velocity, and Phase velocity [duplicate]

Mathematically, you find that the wave function of a particle $\Psi (x,t)$ moves with the same velocity as the velocity of the particle ($v_{particle} = v_{group}$). Is there a reason why the ...
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Dispersing ultrasound in a tube - patters

I am looking for patterns to efficiently disperse reflected ultrasound in the range of wavelengths 1mm to 4mm within the interior of a narrow tube (I do not want wall reflections). For various reasons ...
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Refractive index variation with colors [duplicate]

To explain the spectrum formation in the prism, my teacher said that different colors have different speeds in a medium, so, refractive index is different for all. So, angle is different. But I don't ...