Rayleigh Definition and 108 Threads

Hello! I have the following situation: I have a 3 level system, with 2 ground states, call them ##g_1## and ##g_2## and an excited state, ##e##, with energies ##E_{g1}<E_{g2}## and ##E_e##. I have a driving field with frequency ##\omega## such that ##\Gamma \ll \Delta \ll E_{g2}-E_{g1} \ll E_e -...

From posts like this I get that the color of the sky is explained by Rayleigh scattering, but needs density fluctuations. However as atoms are not uniform and are localized, the density is $$\rho(\mathbf r)=\sum_i \delta(\mathbf r-\mathbf r_i)$$ where ##i## sums over all the atom positions...

Folks, I'm trying to formulate the stability problem in the incompressible inviscid limit and find the dispersion relation in the Couette flow regime. As shown, the 2 infinite plates move one against the other, unlike the "standard" case where one plate is static and the second moves. I'm trying...

I have a little question about Rayleigh scattering: I know that Rayleigh cross section is proportional to the inverse of the fourth power of the wavelenght of the incident light and that it is so even the intensity of the scattered beam of light, now: 1. What is the color of the sky due to...

answering part ccould someone explain each region of diagram. thanks. I've got parts a and b correct

Hi PF! Say we have the variational problem $$M[\phi(x)] = \lambda K[\phi(x)]$$ where ##\lambda## is the eigenvalue and ##M,K## are linear integro-differential operators. Now given a set of basis functions ##\phi = \sum_j c_j \phi_j##, is this simple enough to conclude that eigenvalues...

What is the application of each of them?

We know ##\lambda_{blue} < \lambda_{red}## so citing the formula above (in the relevant equations) it's apparent that blue light is scattered more than red light. But presumably this would hold for ##\theta = 0## as well but when we look at the sun head on we don't see blue, we see red/orange...

I have tried this question and have gotten to an answer from the following steps So my angular separation is 2.85 millidegrees. Have I done this right with the formula I have made use of? Any help would be great, thanks!

I have been trying to numerically solve the Rayleigh-Plesset equation for a sonoluminescing bubble in Python. You can read about this phenomenon here: https://iopscience.iop.org/article/10.1088/0143-0807/34/3/679. The Rayleigh Plesset equation is a non-linear ODE, which can be solved to find...

I have been trying to numerically solve the Rayleigh Plesset equation: $R\ddot{R} + \frac{3}{2}(\dot{R})^2=\frac{p_g-p_0-p(t)}{\rho_l}-4\mu\frac{\dot{R}}{R}-\frac{2\gamma}{\rho_lR}$ using the odeint python function. The code is given below: import numpy as np from matplotlib import pyplot as...

I'm pondering the behavior and persistence of rocket exhaust plume molecules far above the atmosphere. For example, the plume from an apogee circularization thrust from GTO (Geosynchronous Transfer Orbit) to GEO (Geosynchronous orbit). CO₂ and H₂O are among the molecular species emitted by a...

I was reading that in inverse scattering approach, we divide the region of interest into discrete grids and size of each grid should be much smaller than the incident wavelength (usually smaller than one-tenth of wavelength). By this logic, theoretically, I can use inverse electromagnetic...

Hi everyone, does the scattering irradiance ratio between blue/red change with distance with Rayleigh scattering? I would think that it would remain generally constant..

Hello, I'm trying to find out the distribution function (cumulative or density) of the product of two independent random variables respectively following a non-zero-mean Gaussian and a Rayleigh distribution. The math is too intricate for me, I've found in the appendix of [Probability...

Hello, Context is Inverse Compton Scattering with an pulsed electron beam interacting with a pulsed laser. A laser has a Raleigh length of Z_r = w_o^2 * pi / lambda w_o is the the radius of the spot size, lambda is the laser frequency. I want to match this spot size to a pulsed electron bunch...

By comparing the given equation to the equation for the Sturm-Liouville form, I see that p(x) must equal 1, q(x) must equal 0 and sigma(x) must equal 1. After this, I have no idea what I should be doing for part 2.

Hi everyone, this is sort of a soft question which I need to ask to make sure my understanding is correct, it relates to a little project I'm doing on measurement resolution. The first question is to clear up a general concept, the second is based on the first and is the actual question...

Good day, I do not fully understand the physical mechanism of formation of Rayleigh waves at the free surface. While their derivation is quite clear and obey free-boundary conditions, it is not clear their physical mechanism. Could you please correct me in my discussion. Incident P-wave can...

What will change if we place the slips in front of the converging lens instead of behind the collimating lens? My teacher say nothing will change in the interference pattern but I doubt his answer.

I've read that UV light cannot "penetrate" the atmosphere as easily during winter. But what does this exactly mean? My hypothesis is that due to rayleigh scattering, since light with smaller wave lengths scatter more, the UV light doesn't end up reaching the surface of the Earth (i.e. gets...

Hi PF! Given the ODE $$f'' = -\lambda f : f(0)=f(1)=0$$ we know ##f_n = \sin (n\pi x), \lambda_n = (n\pi)^2##. Estimating eigenvalues via Rayleigh quotient implies $$\lambda_n \leq R_n \equiv -\frac{(\phi''_n,\phi_n)}{(\phi_n,\phi_n)}$$ where ##\phi_n## are the trial functions. Does the...

I've been trying to find a proof or a paper that goes into calculating why the sky is blue as opposed to the "the sky is blue because of scattering" explanation that all over the internet. I (think) understand the concept but I would like to see some numbers. I'm aware of the I = 1/lambda^4...

When light enters an ocean, the photons scatter elastic with water molecules yet the presence of opaque particles causes the depth to be limited. Is this scattering Rayleigh scattering? (like the scattering in our atmosphere) https://en.wikipedia.org/wiki/Rayleigh_scattering

Okay, so I just found out about the Rayleigh distribution being the radial distribution of a point composed of normal distributed cartesian components. And this is because of the area element, right? But how then can the joint density of the cartesian component's distributions equal that of the...

Hello, I am having a bit of trouble understanding the concept of Rayleigh scattering as it relates to light from the sun. My book states that unpolarized light will hit the atmosphere, and the scattered light will be mainly horizontally polarized, while the unscattered light remains...

Hi, I have read about the rayleigh sommerfeld integral and its a surface integral. Why is it difficult to calculate the integral directly?

Rayleigh scattering is what caused the sky to be blue.. what elements must be replaced to make the sky orange, or yellow or other colors? Is there a list of elements somewhere for the different colors?

Why a fluid jet becomes unstable only when the wavelength of the perturbation exceeds the value of jet perimeter? Do you imagine any physical reason behing this?

How can you tell where a dispersed Rayleigh wave train ends...? Is there a way to identify the end of a Rayleigh wave train on the following teleseismic records? The first shows the full surface wave train, the second is zoomed in but cuts off the final part of the original including the last...

My question stems form the section "How Many Modes in a Cavity?" in the following derivation of Rayleigh-Jean Law: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html#c2" In here, they count the number of modes as represented by volume of an eighth of a sphere. What's the mathematical...

Is there some way to - from an intuition standpoint - justify the fact that there should be a factor of ##a^{6}##, (where ##a ## is the particle diameter) in the Rayleigh Scattering formula? I've seen a few sources hint that there should be. I can follow the derivation from e.g a Lorentz atom...

Homework Statement 'A scientist wants to take a picture of a distant yellow object using a pinhole camera such that the picture is of maximum sharpness. Let ##\lambda## =wavelength of yellow light, ##d## = diameter of pinhole, ##D = ## distance of pinhole to film. Find ##d##. Homework...

Homework Statement ii)Rayleigh method gives me inverse of expected result.Would really appreciate your help. Homework Equations show that ##f(gamma)##=##(\frac {ro*R^5} {E*t^2})## where ro=density R=radius E=energy The Attempt at a Solution We will do dimensional analysis on the elements...

Homework Statement "A source emits light with two monochromatic components of wave-lengths λ1 = 510.50 nm and λ2 = 510.90 nm. Using the Rayleigh criterion, find the minimum number of slits of a grating that must be illuminated by a beam from the source in order to resolve these components."...

G'Day Everybody, I am computing buckling of a rectangular(edges: a*b) specially orthotropic composite plate. The boundary conditions are clamped-clamped at the opposing loaded edges and the other two edges are free (also known as CFCF). After having the boundary conditions and the governing...

From a book intro I've been reading, Scattering, Absorption and Emission of Light by Small Particles by Mishchenko, it states that when incident light hits a particle, that particle may absorb light, scatter light or emit the light. Excerpt: Can anyone explain to me, on a physical level, the...

I heard that the analysis of wave measurements close to shore verifies that as long as wave amplitudes are small with respect to mean depth a Rayleigh distribution remains satisfactory of wave heights, but how ?

Homework Statement \[/B] The question I want to ask is how do you relate conditions such as To* and To,1 and To,2, where To,1 and To,2 are the stagnation conditions at the entrance and exit. This is the problem I was doing. Standard atmospheric air is drawn steadily through an isentropic...

Regarding Raleigh Scattering (Wikipedia) "The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation we see as scattered light" Please anyone give simple...

Homework Statement I have a quantity in Rayleighs and need to convert it to dB. Homework Equations Intensity Reflection Coefficient R=5.625 x 10^-1 Rayls. dB? The Attempt at a Solution None so far-please advise. Thanks.

Homework Statement (iv) Calculatethehistogramforthewaveheightandwaveperiod.(v) Compare the histogram with the Rayleigh distribution.(vi) Calculate exceedance probability distribution for the wave height and wave period using plotting position formulae and compare it with Rayleigh...

Hello, I am trying to calculate the surface cooling rate from the sides of a round tin can using Rayleigh, Prandtl and Grashof numbers but I'm getting a ridiculously high result, and I'm hoping someone could run through my numbers to tell me where I'm going wrong. Posting my question is...

Hi I'm trying to model the drag effects in using Lagrange Mechanics and trying to include the effects of aerodynamic drag. I've read up on the Rayleigh Dissipation functions in Greenwood's "Advanced Dynamics" and a few other books but they always provide the Rayleigh function for drag forces...

Hello! I apologise, if I put this problem into the wrong topic. I know that when the light is shined on the molecule it can get polarized. And because of that you can get Rayleigh and Raman scaterring. Also I know that only one photon over million or billion will scater as Raman. The...

Homework Statement I must compare the diffraction limit of the Hubble telescope (2.4 meter) observing 500nm and a 100m telescope observing radiowaves with a wavelength of 21cm. I am asked to then explain why radio telescopes must be bigger! Homework Equations The Attempt at a...

How is the number of oscillations per unit volume in the frequency range of v and dv is (8v^2*dv)c^3 where c is the velocity of light

Hi @ all, i want to simulate the cooling behavior of liquid aluminum in a vertical cylinder(simplified geometry of a real transport crucible), the cylinder is cooled down by the surrounding air from all sides, from top and from buttom, i expect free convection in the liquid to simulate...

Hey guys, I was hoping someone could set me straight on the two main methods of calculating shaft critical speeds. I have a final coming up but I can't seem to get these two to agree. What I know: -Dunkerly underestimates, Rayleigh overestimates -Deflections used in Dunkerly are those...