Dispersion Definition and 261 Threads

Assuming that light travels through an optically dense medium such as glass slower than in a vacuum: 1. What on the atomic level causes the different changes in speed for different wavelengths? 2. For a light wave incident at the normal (90 degress) of the entry boundary do the different...

I'm doing a literature review on dispersion relations, and I've been told that if i can derive the phonon dispersion relation, it would help my review. So i was wondering if anybody could help me with the derivation either through Quantum-mechanical approach or Semi-classical treatment of...

Hello, I would appreciate very much some help on this problem. I have a Hernquist model (distribution function) and I am trying to generate equal mass initial conditions. The way I do it is this. I have the mass profile M(r) and I pick say 10^6 random numbers between 0 and 1=M(r->inf). Then I...

Homework Statement The conductivity of a plasma is defined as \sigma = i\frac{Ne^{2}}{m\omega} where N is the electron density. a) Prove the refractive index is: n = \sqrt{1- (\frac{\omega}{\omega_{p}})^{2}} with \omega_{p} = \sqrt{\frac{Ne^{2}}{m\epsilon_{0}}} b) Show the Attenuation...

Homework Statement Given the dispersion equation of an electron in an electric field: Homework Equations a) calculate the velocity of the electron if k = π/a b) If the electric field E is applied in the -x direction, derive the time dependence of k for an electron initially at k...

Homework Statement I saw this question on this forum and the answer given At first I thought that it was obvious why reducing the width of the fibre would reduce the multipath dispersion. But having tried the problem with maths, I'm not so sure. Can anyone tell me where my maths...

Does anyone know of any data regarding mass dispersion around Earth? That is to ask (more toward my interest), if the observable universe was broken into equal 3-D sections like "North to Northeast" "NE to E" "E to SE" and so on... would the mass of each section observed from Earth be equal...

hi, lately i am concerned with Van der Waals forces and I often found in chemistry books the so-called London dispersion force, which says that the potential energy of the Van der Waals interaction is: U=-2/3 a1a2I1I2/(r^6*(I1+I2) but by now I could not find a theoretical derivation of...

Hello, I am constructing a 2d atomistic mass spring Hamiltonian with nearest neighbor bonds (harmonic potential) in an attempt of calculating the phonon dispersion. I solve the eigenvalue system and calculated the eigenvalues or phonon energy levels (y-values of dispersion). I am fine up to...

Please Help :) "Calcium H and K lines have rest frame wavelengths of 3968.5 A (angstrom). Spectroscopy of 5 stars in a cluster revealed that the Ca H line was detected at 3970.1 A 3966.3 A 3967.5 A 3971.0 A 3968.2 A in each of these five stars. Calculate the line of sight velocity dispersion of...

Hi I'm trying to get a better understanding of dispersion in light. Specifically, the relationship between refractive index and wavelength, and why the refractive index increases for decreasing wavelengths. However, I've been confused by all the various information I've come across...

In anomalously dispersive media, the change in phase velocity with wavelength is negative; that is dv/dλ < 0. I wanted to ask: (a) whether you could fit a wide range of frequencies into a resonant cavity by taking advantage of anomalous dispersion (b) whether a material like this exists...

I’m wondering why standard deviation is used as the main method of measuring dispersion, when i would consider that more ergonomic (user friendly) measurements are possible. An example of such would be, the sum of |x-mean|/ n . I would think that the mean plus and minus this value would...

Hey ppl, I have a question for you. For the case of light propagation in the air the the group-velocity dispersion parameter D is infinity because the derivative of the group velocity should be a zero (group velocity is constant ; w=ck and Vgroup=dw/dk). Who can explain me this? dispersion...

Hi In litterature, I have noticed some authors write the dispersion for the d-wave gap as Δ(k)=Δ[cos(kx)-cos(ky)]/2, and some write it as Δ(k)=2Δ[cos(kx)-cos(ky)]. Where does this difference come from?

Really struggling with this question guys, any help/advice will be greatly appreciated. Thanks in advance! Homework Statement Sketch dispersion relations for, (i) a proton (ii) a free electron (iii) an electron, in a crystalline solid. Comment on the similarities between (ii) and...

Sry for a proper wall of text, and it´s probably pretty "chatty" too, as I reason about things back and forth... Plz do feel free to comment on the reasoning since I post it to learn how to think about these things... I believe that I have sometime learned that one can relate refractive index...

I was just looking at an expression (a dispersion relation, omega^2 = ...) similar to that of warm electron's in a plasma http://en.wikipedia.org/wiki/Plasma_oscillation expect with an extra imaginary term, which I think comes out from the full derivation of the dispersion relation for warm...

Hi I am reading and trying to comprehend the article "Dispersion of soluble matter in solvent flowing slowly through a tube", Sir Geoffrey Taylor, Proceedings of the Royal Society of London, 1953. I am particularly interested in cases A2 and B2, where a concentrated solution is injected...

Hello all, What does it mean when two phonon branches get crossed in phonon dispersion relation ? Also, in certain high symmetry direction, one can find only one transverse branch and other direction two separate branches, what do these response mean? (Ref. Solid state physics by...

I have searched this topic in our forums. no answer about that. I have obtained the phonon dispersion curve by applied a numerical simulation. However, how can I obtain the phonon density of state from such a curve? generally speaking, g(q)dq = g(w)dw, here q is the wave-vector; w is...

Can someone please explain the difference between Material dispersion and waveguide dispersion?

I'm having a wording issue in a paper I'm writing. Specifically, I'm trying to decide between arguing something is "diffusion" vs. "dispersion". Can anyone point me to a reference that clearly demarcates between these? In specific, I'm referring to the diffusion/dispersion of an injected drug...

Hi there So I was looking into group velocity and related matters and found myself quite confused. So now I have a few questions which I feel I need to understand (primarily the first one). Any help with these would be awesome and I would be very grateful... 1) Why is the group...

I'm curious why electrons will travel near the perimeter of a large wire as opposed to using the whole cross section. I understand that electrons flowing through the wire repel each other and thus want to be as far apart as possible. Yes, but from this electrons should not just occupy the...

Hi I am reading about dispersion and index of refraction, and I have encountered the term "anomalous dispersion". This is where dn/dω<0, and where the absorption is strongest because of damping. Now, I can't seem to connect those two dots (and my book does not explain it nor Wiki): Why does...

I am having trouble understanding a basic problem in fluids that came up during an exam I took last quarter. Namely, we are given a dispersion relation and asked to quantify how a one dimensional surface disturbance propagates in space. (The disturbance is initially an approximate delta function...

*for a group of waves, the energy is transmitted with the group velocity. what does that mean? *what is meant, as in actually meant, by dispersion of a wave in a medium? whatever i looked up says phase velocity depends on frequency for a dispersive medium and vice versa. Why? * wave...

Hi guys, I'm looking for some references where dispersion relations, say for photons, are explicitely written out in a generic medium. In other words, the dispersion relation for particles not propagating in the vacuum is a different one than the standard vacuum one E^2 = p^2 + m^2 and I'm...

Can anyone explain "dispersion" to me in simple words? Can anyone explain "dispersion" to me in simple words? like,, when waves escape from a small gap why would they s[read out in circles? thnx for help!

Hi I'm trying to sort this concept out in my head and have reached a stumbling block! 1. ok so light travels through medium a and transmits through medium b and refracts. The angle or refraction is given by snell's law, and quantified by the refractive index of materials a and b. 2. But I...

Hi All, In quantum mechanics, related to photon, we have these two equations as valid ones: E = h x f p = h / lambda But we have in vacuum the dispersion relation c = lambda x f. 1) How these relations change when the dispersion relation change ? 2) Is it universally correct to...

In which case would water fall out of the tank faster? 1) If I were to take a tank filled with water and bore a large hole in the bottom of it with some area 2) Riddle the bottom of the tank with small holes that have an area that adds up to the area of the first big hole. In one scenario...

Hi, I'm trying to take this Sellmeier equation, n^2 (λ)=1+ (B_1 λ^2)/(λ^2-C_1 )+(B_2 λ^2)/(λ^2-C_2 )+(B_3 λ^2)/(λ^2-C_3 ) for which i have several sets of constants for prospective glasses, and convert it into a group delay dispersion graph, with axes of fs^2 vs wavelength. How do i...

In a question about dispersion using an equilateral prism, three blackened bulb thermometers were used. One was placed above the red light, one on the green light and the last one below the violet light. The question was ... Give 2 reasons why the highest temperature would be recorded...

Hi, being a skeptical MD (radiology), I'd like to have a physicist's view on a chiropractic mechanical device called the "Activator" (http://activator.com/, http://www.youtube.com/user/drcherok, http://www.youtube.com/watch?v=knM5dx2tFH0&feature=related), which in my view is a worthless and...

Does dispersion of light by a prism have anything to do with how thin films disperse light of different colors at different angles? Could a person imagine the sides as if they were thin films?

Hi. What I'm trying to do is to obtain the energy spectrum from the following dispersion relation: E^4-A·E^3+B·E^2-C·E+D-F·E^2·cos(k·a_0)^2+G·E·cos(k·a_0)^2-H·cos(k·a_0)^2 = 0 where E is the energy, k is the wave vector and a0 the distance between adjacent neighbors in a 1-Dimensional...

Derivation of velocity dispersion from virial theorem?? Hey, Im probably being a bit dim here but could anyone help me derive the velocity dispersion from the virial theorem. I've got 2K+U=0, K/m~sigma^2 and U/m~GM/R. From rearranging I get a negative velocity^2? Or maybe its the...

Let us assume we possesses a line radiator. It's extent is infinite and it radiates 360*. As far as I understand, an expanding spherical wave of order 0 is not dispersive. I assume an expanding cylindrical wave of order 0 would possesses dispersion, however I am not certain. Could any...

Homework Statement White light containing wavelengths from 396 nm to 756 nm falls on a grating with 7300 lines/cm. How wide is the first-order spectrum on a screen 2.15 m away? Homework Equations y=m*L*wavelenth/(d) The Attempt at a Solution using the equation I have found y1 to...

(I would like to put an idea of mine to rest) About one year ago I took a college chemistry course in which I learned about intermolecular forces. The weakest of these intermolecular forces, I learned, was the dispersion force (also called London force). This force was discovered by Fritz W...

1. Calculate the velocity dispersion for hydrogen atoms in the solar photosphere, which has a temperature of 5800 K. 2. I know no equations to solve the problem. 3. I have no idea any method of going about solving for velocity dispersion. I would appreciate any guidance. Thanks

Ok so here's another problem that i just completely don't understand at all. Thanks for your help. A linear chain consists of 2N equally spaced identical particles with mass m and speration a, coupled by springs with alternating constands k1 and k2. Use the periodicity of the system to find...

what can be interpret from dispersion curve of phonon?how to find whether a phonon can loose all its energy to a neutron from dispersion curves?are there dispersion curves for other atom apart from phonon?

Hi guys, I just have a short question. A prism splits white light into it component color depending on the wavelength of the color. As the wavelength decreases, the index of refraction increases, so the wave bends more. However according to Snell's law, a greater index of refraction results in...

if i don't want to understand the white light as a pack of waves that when encounter prism the waves start to unpack, but as a photons, but than i can't see how it's working, i mean. what is happening to the photons when they enter a prism? thanks

Hi guys, I don't understand how one would exactly determine a dispersion relation of phonons experimentally. There are two equations, one for momentum and one for energy conservation: \vec{k} - \vec{k^{'}} = \vec{G} + \vec{K} \omega - \omega ^{'} = \omega(K) where...

can some one explain what chromatic dispersion is? and it helps me finding which colour radiates more heat in the given spectrum.

Does light exhibit any type of dispersion in a vacume?