What is Dispersion: Definition and 284 Discussions

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.
Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity.
Although the term is used in the field of optics to describe light and other electromagnetic waves, dispersion in the same sense can apply to any sort of wave motion such as acoustic dispersion in the case of sound and seismic waves, in gravity waves (ocean waves), and for telecommunication signals along transmission lines (such as coaxial cable) or optical fiber. Physically, dispersion translates in a loss of kinetic energy through absorption.
In optics, one important and familiar consequence of dispersion is the change in the angle of refraction of different colors of light, as seen in the spectrum produced by a dispersive prism and in chromatic aberration of lenses. Design of compound achromatic lenses, in which chromatic aberration is largely cancelled, uses a quantification of a glass's dispersion given by its Abbe number V, where lower Abbe numbers correspond to greater dispersion over the visible spectrum. In some applications such as telecommunications, the absolute phase of a wave is often not important but only the propagation of wave packets or "pulses"; in that case one is interested only in variations of group velocity with frequency, so-called group-velocity dispersion.

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  1. adamaero

    Dispersion relation ~ modern phyics (solid state physics)

    Homework Statement Which cannot be the structure of two acoustic branches, nor three acoustic branches? Simple cubic, FCC, BCC, diamond cubic, NaCl lattice Homework Equations N/A http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61...
  2. J Azeez

    A Velocity Dispersion: Meaning & Difference Explained

    What does mean by velocity dispersion of galaxy? What is the different between stellar velocity dispersion and molecular velocity dispersion?
  3. DaTario

    I Dispersion Relations: Most Famous DR & Contexts Explained

    Hi All, The equation: ## v = \lambda f ## is presented as a dispersion relation (DR) for it is a formula that specifies the velocity of a wave of certain frequency. This equation seems to be the most famous DR in physics. My questions are the following: What is the second most famous DR? Which...
  4. otaKu

    Solid State A good book to learn about phonon dispersion relation

    So I see them in the books labelled as accoustic and optical phonons but I don't seem to find a comprehensive treatment of the matter for a beginner who doesn't know a thing about the dispersion curves. I'd prefer not to dwell too much into the mechanical treatment if possible since I just need...
  5. jksy

    A Understanding the Impact of q=0 on Spin Entropy in FM and AFM Magnon Dispersion

    How calculate the DOS from the one dimensional AFM and FM magnon dispersion relations given in Kittel? What is there limiting form as q -> 0, and how does this affect the spin entropy?
  6. A

    PFR with axial dispersion - CSTR in series conversion?

    Homework Statement Here is the problem description: Develop an Excel file that given a set of data from an RTD pulse injection will determine the model parameters of the following schematics, and then predict the conversion in a CONTINUOUS reactor with a n-order reaction (where n is not equal...
  7. chikou24i

    A Acoustic and optical branches in phonons dispersion curves

    What is the physical meaning of acoustic and optical branches in phonons dispersion curves ?
  8. G

    I Do non-monochromatic "waves" exist in dispersive media?

    Hi. Is the superposition of two different monochromatic waves in a dispersive medium still a wave (i.e. a solution of a wave equation) if the phase velocity is not the same? Since the wave equation contains the phase velocity, the two individual waves are solutions of different wave equations...
  9. M

    I Dispersion relation of a transmission line - questions

    Hi, I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another...
  10. M

    Focal length of diffraction grating for recip. dispersion

    Homework Statement What would the focal length be of a diffraction grating if the set up is a laser placed 1 m from the 0 order diffraction? Would it be the distance from the grating to the laser or the distance from the grating to the image? Homework Equations 1/f = 1/o + 1/i Rd = [Df]-1...
  11. Anithadhruvbud

    Differences between dispersion and scattering?

    What makes dispersion be different from scattering? What exactly is the definition of scattering? Google says it is to deflect or diffuse.how can deflection be a synonym for scattering? How are they related?
  12. bcrowell

    Dispersion of gravitational waves

    The LIGO paper https://dcc.ligo.org/LIGO-P150914/public puts limits on the dispersion of gravitational waves, which can be interpreted as an upper limit of 10^-22 eV on the mass of the graviton. We all know that low-amplitude gravitational waves are supposed to propagate at c according to the...
  13. E

    Another question about dispersion (and wavenumber)

    Hello! I still would like to thank those who participated to my previous thread about group velocity and dispersion. Now there is a (maybe) simpler question. A sinusoidal, electro-magnetic plane wave in the vacuum propagates in a certain direction with the following wavenumber, which is supposed...
  14. N

    MHB Solve for frequency & angle in dispersion equation

    OK I'm about to grow (more) gray hairs... Could some friendly soul smarter than myself kindly help me solve for both f and theta respectively in the following equation, please: x = sin[ (pi*f*W)/c * sin(theta) ] / [ (pi*f*W)/c * sin(theta) ] Getting stuck at "arcsin of arcsin" sort of...
  15. C

    Graphene energy dispersion & density of space relation PD

    Hello, What is the energy dispersion relation and density of states for graphen near the Dirac point ? I am looking for a proper graph illustrating these properties.
  16. G

    I Theoretical explanation for Dispersion? (Sellmeier)

    One of the most accurate formulas for dispersion is the Sellmeier equation: n^2(\lambda) = 1 + \sum_i \frac{B_i \lambda^2}{\lambda^2 - C_i} Dispersion does not arise with Huygen's Principle. Is there a theoretical model that describes dispersion and explains why Sellmeier's equation takes the...
  17. C

    Relation between electronic band structure and Fermi energy

    I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
  18. A

    Dispersion operator in quantum mechanics

    I am a beginner in quantum mechanics and I am confused about the operator ΔA defined to be ΔA Ξ A - <A>. Can someone please tell me how to interpret <A>? From what I can understand, <A> is the expectation value and is defined to be <Ψ|A|Ψ>. But that is just a scalar correct? How do subtract a...
  19. J

    Phonon dispersion Points/Modes question

    Hey all, I am trying to recreate the phonon dispersion plot of the paper below http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-730-physics-for-solid-state-applications-spring-2003/projects/ProjP21.pdf The problem is I do not know what the Tau, L, and X on the x-axis...
  20. sounouhid

    Dispersion Energy in Semi Conductors: What Is It?

    can anyone tell me what is the dispersion energy in semi conductors
  21. M

    Are there exceptions to the rule of speed and energy for waves?

    Today I was presented with dispersion in my introductory physics class. Before this topic was presented we were told of two important rules for waves: 1) The speed of a wave is dependent on the medium in which it travels and 2) the frequency of wave does not change when going from one medium to...
  22. norlesh

    Would a flattened (sheet glass) dispersion prism work?

    Could a thin sheet of glass with appropriate edge angles work as a dispersion prism? If the prism were laying flat my thoughts are the light should be contained via TIR in a plane that would remain perpendicular to the top and bottom while said plane dispersed horizontally according to...
  23. I

    Dispersion and the dependences of refractive indexes

    I'm revising for a uni exam with past exam papers, and have gotten stuck on the details of dispersion. The two exam questions prompting this are a) What is the physical reason why the index of refraction for blue light is bigger than that of red light? and b) Explain how dispersion makes a...
  24. Rrrenata

    The energy dispersion relation for sc, bcc and fcc?

    Homework Statement I need to calculate the energy dispersion relation in the tight binding for simple cubic, base centered cubic and face centered cubic crystals. There are no values given, they just need the result depending on the lattice constant a. Homework Equations E (k) = alpha + beta *...
  25. K

    Dynamical matrix and dispersion

    Dear all, In this paper: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.125402 In the appendix the author attempts to arrive at the spectral density of states of the surface of a half-space. To do this, he arrives at the Green's function of the surface atom of 1D atomic chain and...
  26. evinda

    MHB Solve Dispersion Equations: Wave Solutions

    Hello! (Wave) I want to find the dispersion relation for the solutions in the form $u(x,t)=e^{i(kx-\omega t)}, k, \omega>0$ of the following partial differential equations: $u_t+au_x=du_{xx}$ $i u_t+u_{xx}=0$ $u_{tt}=au_{xx}$, where $a,d>0$. Which of the above equations are dispersion...
  27. D

    Dispersion relation for non-relativistic quantum particles

    In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...
  28. W

    Dispersion relation for diatomic linear chain.

    Hi. Here's the dispersion relation for a diatomic linear chain, where the distance is a/2 between each atom. My issue here is that if you set m_1=m_2=m, i.e. set both atoms equal to each other, it doesn't automatically reduce to the old acoustic dispersion relation as the ± term doesn't...
  29. B

    Tight binding dispersion for graphene

    Hi I have Hamiltonian matrix and overlap matrix. How to calculate tight binding dispersion for graphene in matlab? I would be appreciated if could some one give me a hand on my problem.
  30. C

    Dispersion relation for the free electron model

    I'm trying to get my head around what this means exactly. I've plotted the graph to help verse me with the functions that I've derived. From the free electron model, the wavefunctions are treated as planewaves of the form \psi_\mathbf{k}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} Due to...
  31. R

    Wave dispersion and the bandwidth theorem

    Homework Statement Consider a propagating wave packet with initial length L0. Use the bandwidth theorem to show that the minimum range of angular frequencies present in the wave packet is approximately: \begin{equation} \Delta \omega = \frac{v_{g}}{L_{0}} \end{equation} where vg is the group...
  32. U

    Dispersion relation and their origins & meaning

    Hi Everyone, I'm trying to understand dispersion relations in general. I know that for a simple wave like a light wave there is a 'constant phase' so the dx/dt is equal to the ratio of the angular frequency (omega) by the wave vector (k). However what does a 'constant phase' mean? How can I...
  33. synMehdi

    Speed of EM wave depending on the frequency

    I know that in a vacuum, speed of light is constant. My question is more about the speed of light in a material like air. Dispersion of light in a prism tells us that the speed of light or the material index depends on the wavelength ( or frequency which is constant ) so I thought that air...
  34. R

    How to simplyfy a square root term? Phonon dispersion relati

    I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...
  35. N

    Lattice wave dispersion relation

    Hi. A very quick question. Why is it impossible for a wave to travel on a linear one-atomic chain if its wavelength equals the lattice constant? I.e. the lattice points vibrate with a wavelength equal to the distance between them? Here's what I mean...
  36. L

    Diffraction Grating and Dispersion

    1. The problem statement A diffraction grating has a slit separation of 2094.0 nm. What is the dispersion of the 2nd order lines at an angle of 30 degrees (in degrees per micrometer)? Homework Equations dsinΘ=mλ y=(mDλ)/d 3. Attempt at a solution I began by finding λ using the first...
  37. C

    Where does the temporal stretch come from in Group Velocity Dispersion?

    Homework Statement Our lecturer seemed to skip over how to get from the Group Velocity Dispersion to the actual temporal stretch of a pulse sent down an optical fibre, instead we were given just the two formula. I've been trying to work out where the temporal stretch comes from but can't work...
  38. Robsta

    Distance to pulsar with plasma dispersion relation

    Homework Statement Pulsars are stars that have suffered gravitational collapse. They rotate rapidly and emit a narrow beam of radiation. The pulse lengths, at the earth, are ∼1ms and the periods are ∼1s. Within a few months of the discovery of pulsars distance estimates were obtained by...
  39. C

    Dispersion Relations (tight binding energy)

    The nearest neighbour tight-binding energy band for an fcc metal can be written as: E(kx; ky; kz) = Ei - A - 8t[cos(pi*kx)cos(pi*ky) + cos(pi*ky)cos(pi*kz) + cos(pi*kz)cos(pi*kx)]where kx; ky; kz are express in units of 2*pi/a . Sketch this band dispersion (a) between the (capital Gamma) point...
  40. aditya ver.2.0

    Can dispersion of light take place through lens?

    Can dispersion of light take place through lens, i.e. can lens (incl. Convex and Concave) scatter white light into its constituents?
  41. H

    Dispersion relation (particle in a box)

    I am learning some basic solid state physics idea, like density of state ...etc. For particle in a 1D box, E = n^2 (pi)^2 (h_bar)^2 / 2mL^2 But why it is written as E = (h_bar)^2 k^2 /2m does it means that energy eigenvalue E is related to momentum k ? I guess it is not because momentum is...
  42. S

    Pairwise velocity dispersion in Cosmological simulations

    There are numerous publications about pairwise velocity dispersion ( PVD ) of galaxies in real redshift surveys. It is customary to use an exponential form for the distribution of pairwise velocities and then model the redshift space distortions in the 2PCF to retrieve the PVD. Now if i have a...
  43. C

    Snell's Law: Dispersion Light Angle Refraction

    Homework Statement A red beam of light in air enters crown glass at an angle of 60.00 to the normal. Find the angleof refraction. Repeat for a violet beam oflight entering crown glass (same angle). Homework Equations Not too sure, I believe I would use Snells law here.. does that sound...
  44. G

    Help needed to understand dispersion curve of a 1D lattice with diatomic basic

    Hi there, I am trying to understand the dispersion curve(as shown below) of a 1D lattice with diatomic basic. Here are my questions 1) Can both optical and acoustic branch of phonon can simultaneously exist in crystal? 2)Why there is a band gap between optical and acoustic phonon...
  45. M

    Dispersion of light through a prism and block, changing the incident angle

    There was a question in one of my study materials that asked if you increased the incident angle of white light striking the surface of a glass prism, would the colors disperse less or more. The answer was disperse more. I didn't have an answer because I saw a conflict between the two...
  46. R

    Nonlinear Dispersion Relation with Imaginary Part

    Homework Statement I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let k=\alpha+i\beta and solved for \alpha and \beta I found that there are \pm signs in the solutions for both \alpha and \beta...
  47. gfd43tg

    IPhone camera light dispersion

    Hello, I am working on a project where I am trying to take a photo of paper that I insert into a slot of an iPhone cover that I created with a 3D printer. My goal in this stage of design is to be able to take a photo that will disperse the light evenly across so that the lighting is uniform...
  48. A

    Band Dispersion and Career Mobility

    how the dispersion relation(i.e. E-k relation) affects carrier mobility in metals or semi-metals?
  49. applestrudle

    Group velocity dispersion and normal, anomalous dispersion?

    From my understanding, normal and anomalous dispersion are because the phase velocity is a function of k so it is different for different components of a group so the group will spread out over time. So what's group velocity dispersion? Is it the same affect (dispersion/ spreading out)...
  50. adjacent

    Why Distant Objects Appear Dimmer: Exploring Inverse Square Law

    Homework Statement This is not a homework problem but I'll post it here.It's just a question that came to my mind. Why does distant objects appear dimmer? The Attempt at a Solution My answer would be the inverse square law. For a point light,it can be quite easy to explain.As the...
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