Rayleigh Definition and 108 Threads

Hello. I am currently studying scattering theory in detail for my BSc thesis, and I'm starting with Rayleigh scattering. I'm following Scattering of electromagnetic waves: theories and applications by L Tsang, J A Kong and K-H Ding, which is pretty much what I like in a science textbook...

first question, would there be more rayleigh scattering on neon gas vs air? im wondering if you have a tube of neon gas, and shine a laser through it, will the laser beam become visible? as opposed to shining a laser pointer around and only seeing the dot.

Hi there, I came across the concept of Rayleigh damping. I aqm told it is unrelated to viscoelasticity and as a result is unable to reproduce the behaviour of real materials under harmonic excitation. I can not understand why. Considering for simplicity a 1D setting, a ball of mass...

I must fundamentally misunderstand what the variational method is. According to my textbook, it's used to find the minimum eigen energy of an operator (in particular, the time-independent schrodinger equation). This appears to be synonymous to finding the eigenvalues of the matrix representation...

Homework Statement The atmopshere allows all the colours of white light except the blue one and instead absorbs it. It is then scattered as blue light. However, I don't get why we would see it as blue. Won't the scattered light overlap all the other colours that were not refracted? So...

I was studying Rayleigh Scattering. The theory says that Rayleigh Scattering is approximated to x<<1 where x=(2*pi*r)/lambda where r is the radius of the particle scattering light and lambda is relative scattering wavelength of light. lambda = wavelength of light / refractive index of...

Explanation for Rayleigh Criterion?? I just want to ask what is the reason behind Rayleigh criterion which states that items are just resolved when the maxima of a diffraction pattern coincides with the first minima of the other diffraction pattern. I have tried finding the answer but to no...

So compton scattering is where x-rays (or gamma rays) collide with an electron and sends it flying. In the process, the incident photon loses energy and is converted to a lower wavelength. According to wikipedia, Rayleigh scattering is the scattering of photons by particles which are much...

Hello there, I am reading this article: http://nis-lab.is.s.u-tokyo.ac.jp/~nis/cdrom/sig93_nis.pdf After chapter 4.2, it mentions some equations for approximating Rayleigh scattering. That is all well, however, it doesn't mention which units of measurement I should use, nor the value of...

Hello! I am looking for the equations to quantile estimation by Rayleigh, Extreme Value Type II Distributions (Frechet Distribution) and Weilbull 2P. I have checked several statistics books and web pages, trying to find those equations but haven't found anything. About Weibull Distribution, I...

Hello everyone, I'm hoping someone will be able to shed some light on what I have to ask. Basically, I'm interested in the reflection of Rayleigh Waves/ Surface Waves as it travels and passes from a free surface to a surface in contact with a liquid. In particular, is there any written text or...

I am doing a Mastering Physics problem that I am stumped on. The question is: "If this resolving power is diffraction-limited, to what effective diameter of your eye's optical system does this correspond? Use Rayleigh's criterion and assume that the wavelength of the light is 550 nm ." The...

There doesn't seem to be any proper online source that describe these flows properly. Please explain the following points that i read about on wikipedia: 1. "The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of...

Hello, I would really appreciate if someone explained to me how Rayleigh scattering works. I understand it as far as knowing that gas particles cause the shorter wavelength light (towards the violet part of the spectrum) to scatter more than the longer wavelength light. This apparently also...

Homework Statement I have two separate problems, but I get the same answer for each. I feel like this must be wrong. Question 1: Find the leading term of a uniformly valid (for t > 0) asymptotic expansion of the solution of the IVP \ddot{x} + \epsilon\dot{x}(x^2-1)+x = 0 \mbox{ } x(0) =...

This isn't a homework question but the professor asked us why someone would choose to set the Rayleigh length of input radiation into an undulator to be the length of the undulator, instead of setting it to be half the undulator's length like normal. The best reason I could come up with is that...

So I have become a bit confused by the relationship between intensity of Rayleigh scattering and density of the gas. Multiple sources (ex. Salby, Atmospheric Physics) give the scattering cross section per molecule, σ, to be dependent on 1/λ4, the index of refraction of the material and 1/N2...

Homework Statement The aim of this exercise is to derive and simulate the error rate performance of binary PSK when the signal is transmitted over a single-path (or frequency non-selective) slowly fading channel. The frequency-nonselective channel results in multiplicative distortion of the...

Welcome Using MLE I found that estimator \alpha parametr from Rayleigh distribution is described by formula \hat{\alpha}=\sqrt{\frac{\sum_{n}^{i=1}x_i^2}{2n}} but I can't proof that this estimator is consistent estimator. Would you be mind and help me with my problem.

Rayleigh criterion and circular apertures-- check my work? Homework Statement Think of the pupil of your eye as a circular aperture 5.00 mm in diameter. Assume you are viewing light of wavelength 550 nm, to which your eyes are maximally sensitive. a) What is the minimum angular separation...

Hello all, I've been working on error analysis of the system, and I finally faced a big problem. Let X~N(mu1, sigma1^2) and Y~N(mu2, sigma2^2), and Z=sqrt( X^2 + Y^2 ) For Z to be a Chi, mu's should be zero and sigma's should be 1, to be a Rayleigh, mu's should be zero and two...

I've seen equations for Fanno flow and Rayleigh flow but I am confused on how to use them properly. Fanno Flow \frac{P}{P^{*}}=\frac{1}{M}\frac{1}{\sqrt{\left(\frac{2}{\gamma+1}}\right)\left(1+\frac{\gamma-1}{2}M^2\right)}...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution I'm really confused as to how to solve this question. What concept does this question have to do with? Thanks again!

Howdy, I'm a computer programmer by trade, but I've got a project I'm working on for fun and could use some help with some of the physics details. I'm trying to get an algorithm that models the intensity 'I' of a monochromatic light at some distance 'd' from the source where there is a...

Hello everyone, I have what should be a simple one to answer. I'm solving for 2 particles in a harmonic oscillator with a gaussian bump in the middle and a delta function interaction. I'm doing all this via Rayleigh Ritz; that is, diagonalizing the Hamiltonian to find the constants in: \Psi =...

Dear all, I am wondering what is the meaning of Rayleigh distribution? I mean in wireless communication channels we often come to a phenomenon called multipath fading, which is complex Gaussian process in nature. When this Guassian process is zero mean, then the envelope (amplitude) of the...

i am reading about Rayleigh scattering in light and have come to understand that atoms absorb light of particular frequencies and then scatter it in different directions. But why do they scatter the light on the first place? Also, why do smaller atoms scatter higher frequency light?

Can someone qualitatively explain the difference between Raman scattering, Rayleigh scattering, and Brillouin Scattering with respect to molecules? I attempt to define each below but would appreciate either affirmation I'm correct or correction if I'm wrong. Raman scattering - Molecules...

is the sky blue because , blue light has more energy so it gets scattered to our eye, and red light has less energy so it gets scattered away from our eye , and when the sun sets the angle the light enters our atmosphere changes , is this similar to white light entering a prism and that...

Hi, I need some really really basic information on Rayleigh waves as the only website I could ind was Wikipedia. This page is too in depth or either not enough information on the basics. So I need much information as possible on how Rayleigh waves work. Thanks.

Homework Statement I need to plot the Rayleigh line for a flow that has the following conditions at one point (Perfect gass assumption holds, R=287 J/kgK, gama=1.4) p = 101.3 kPa T = 300 K s = 6.867*10^3 J/kgK M = .25 My question is what equation am I actually supposed to plot for a...

Homework Statement I need to plot the Rayleigh line for a flow that has the following conditions at one point (Perfect gass assumption holds, R=287 J/kgK, gama=1.4) p = 101.3 kPa T = 300 K s = 6.867*10^3 J/kgK M = .25 My question is what equation am I actually supposed to plot for a Rayleigh...

In some papers and text, it is said that the central spot radius of the Bessel beam (take zeroth order J_0(\alpha \rho), \rho = \sqrt{x^ + y^2} as example) can be estimated to be 1/\alpha. In wonder how to obtain this relation? And does anyone know what's the smallest central spot radius of J0...

I'm wanting to get another optics book. I'm interested in finding a book that gives insight into how light waves interact with surfaces such as in reflection and x-ray diffraction and things like that using sufficient diagrams of the wavefronts and particles and rayleigh scattering. I want to...

I'm just wondering something. Suppose some particles scatter light coming from a monochromatic laser or just some monochromatic light source. I've seen Rayleigh scattering being described as if the particles reemitted light that either added together in phase in the forward direction or was...

Homework Statement A density function used is: f(y) = \frac{2y}{\theta}e^{\frac{-y^{2}}{\theta}} y > 0 using method of transformations find: (a) pdf of U = Y^2 (b) E(Y) and V(Y) Homework Equations f(u) = f(h^-1(u))*|dh^-1/du| h^-1(u) = sqrt(u) The Attempt at a Solution The...

Homework Statement Two points A and B on the surface of the Earth are at the same longitude and 60.0° apart in latitude. Suppose that an earthquake at point A creates a P wave that reaches point B by traveling straight through the body of the Earth at a constant speed of 7.80 km/s. The...

Homework Statement Consider the Rayleigh problem, but allow the plate velocity to be a function of time, V(t). By differentiation show that the shear stress, tau = du/dy*absolute viscosity, obeys the same diffusion equation that the velocity does. Suppose that the plate is moved in such a way...

I am trying to apply the Rayleigh quotient iteration to the matrix A= a 0 0 b where a is different from b (a and b are reals). Find the subsets S of R^2(Reals^2) having the property that the iteration applied to this matrix with initial guesses in S do not converge. Is S a set of...

Would I be right in saying the difference between Rayleigh and Tomson scattering is that Tomson involves scattering off a free electron, whereas in Rayleigh the incident wave is scattered off a bound nucleus? Alos are there any other differences in the two scattering processes? Thanks

Homework Statement I'm not sure but what exactly does the Rayleigh Criterion mean? Also, what does it mean when they say the "resolution" of the image...? Thanks. Homework Equations The Attempt at a Solution

Homework Statement Given a four degree of freedom system that consists of four carts. The four carts each have mass m=1, and they are connected by three springs of constant k=4, 1, 1 respectively. Let x, y, z, and w be the displacement from equilibrium of the four carts, relative to the...

Is it possible to prove the properties of the rayleigh distribution (e.g. mean, variance, std. dev) by hand ?

Homework Statement Let A be a symmetric n x n - matrix with eigenvalues and orthonormal eigenvectors (\lambda_k, \xi_k) assume ordening: \lambda_1 \leq...\leq \lambda_n We define the rayleigh coefficient as: R(x) = \frac{(Ax)^T x}{x^T x} Show that the following constrained problem...

both rayleigh scattering and raman scattering are second order processes the difference is only that the final state of the atom/molecule coindices with the initial state of the atom/molecule in rayleigh scattering, while in raman scattering, the final state is different from the initial...

Why must the size of the particles be much smaller than the wavelength (of say blue light) in Rayleigh scattering? They type that causes the sky to be blue specificly. In Short: How does a small electromagnetic wave size up the size of the entire particle before deciding how it will interact...

Hello Im having 2 questions I'm investigating NIR light propagation in tissue such as the skin and my question is: In dipole aprox: Absorption, emission and normal Raman scattering is one-photon processes. But what is Rayleigh scattering? When light hit a small molecule the dipole...

Hello, This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate. Homework Statement I am taking a course on Viscous Flow, and for Rayleigh flow after applying the similiarity solution : \eta=(y/(2*\sqrt{\gamma*t})) The...

For certain frequencies both Rayleigh and Compton scattering are important. As I could not see the connection between the derivations of the assosciated formulae, I wondered what made a photon "decide" wether it should be subject to one or the other phaenomenon. My reading is that Compton...

Does anyone know a rough ballpark figure for the opacity of the Earth's atmosphere in the visible? Assuming an observer is at sea level looking to the horizon, I calculated the opacity due to Rayleigh scattering in the visible band, as shown in the attachment. I don't really require a high...