All Questions
Tagged with refraction electromagnetism
122
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Diffraction when the wavefront is not parallel to the plane
I am studying Feynman's chapter on the origin of the index of the refractive index (see this link).
If I am not mistaken, what he does is to prove that when a wave enters a medium (modelled as a ...
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1
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Most generic form of refractive index tensors
The refractive index of a material is in general a $3x3$ tensor (as in the case of birefringent crystals). From literature, it seems that in the case of transparent crystals, this tensor is in general ...
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Inconvenience of speed of light in optic fiber
As far as I'm concerned, optic fiber is great in order to transport information quickly using light. Since light needs to undergo total internal reflection every single time it hits the walls of the ...
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Why total reflection happens at only 1 angle?
The critical angle can be intuitively understood by Snell's law.If the incident medium has a bigger diffraction index than the refracted medium then according to Snell's law the refracted ray will be ...
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Definition of the displacement field in classical field Lagrangian
In a BSM related paper (in appendix B), the authors use an effective Lagrangian $\mathcal{L}_{EFT}$, and define the following fields:
$$ \mathbf{D} = \frac{\partial\mathcal{L}_{EFT}}{\partial\mathbf{E}...
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Wave propagation in inhomogeneous media
There is a problem I'm trying to solve for some time now and is about the standard (?) approximation that it is made when one tries to solve the Helmholtz equation in inhomogeneous media, that is
\...
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Microscopic model of complex refractive index
In my Electromagnetic Optics class, we tried to reconcile the microscopic (optical) properties of matter with its macroscopic counterparts, and one of the most challenging properties is the (complex) ...
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On the (variable?) nature of $\epsilon_0$ and $\mu_0$
In electromagnetism, the electric displacement field D represents the distribution of electric charges in a given medium resulting from the presence of an electric field E. Its relation to ...
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Can the refractive index of a medium be negative?(<0)
Recently I was asked in a test what would happen if the refractive index of a medium was negative. Is it possible really? The refractive index is the ratio of the speed of light in a vacuum and ...
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How to derive the effective permeability for split ring resonator?
in Pendry's 1999 paper "Magnetism from Conductors and Enhanced Nonlinear Phenomena", he give the formula of effective relative permeability $mu_r$ of split ring resonator (SRR) which is one ...
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Phase jump at medium border with EM wave
I have been reading a book about electrodynamics and I have stumbled upon the following matter which is, to me , contradictory. When the electromagnetic wave changes medium, it is subject to certain ...
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Effective Refractive index of a mode less than that of the cladding refractive index?
Can the effective refractive index be less than the cladding if the waveguide width is very small. For example for the case of a ~100 nm waveguide.
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Help with dispersion relations for EM waves in anisotropic dielectric materials
I am really struggling to understand the following dispersion relations which we derived in class.
For an electric field in the z-direction, we have:
$$k^2_x + k^2_y = \frac{\omega^2}{c^2}n_z^2\tag{1}$...
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How to use the boundary conditions of electromagnetic waves to derive the refraction law of light?
In my book it says we can use the boundary conditions of electromagnetic waves to derive the refraction law of light. How to derive it?
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How to increase the angle of light (without going from a higher to lower index of refraction)?
I would like a device to spread out/increase the angle of rays in a light source. In other words, I would like to reproduce the behaviour of light traveling from an area of higher to lower index of ...
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When I see a rainbow in the sky, is the full EM spectrum included? does it form a disc and not just a circular arc?
If you could actually see every part of the EM spectrum from a rainbow, would the circle be completely filled in? and would it also extend further outwards from the visible spectrum?
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Simulator to simulate the intereference between light and the wave produced by an electron driven by the light
When an electromagnetic wave reaches an electron the electron will oscillate creating it's own electromagnetic wave which will interfere with the original electromagnetic wave. I am looking for a free ...
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Mass density of photons in a refractive medium
The effective mass density of photons in a vacuum $\rho^{vac}_M$ is related to the photon energy density $\rho^{vac}_E$ by
$$\rho^{vac}_M=\frac{\rho^{vac}_E}{c^2}.$$
Is it true that the mass density ...
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Photon energy-momentum relation inside a material [duplicate]
I understand that the speed of light in a medium like glass, $c_n$, is reduced by the refractive index $n$ so that we have:
$$c_n=\frac{c}{n},$$
where $c$ is the speed of light in the vacuum.
Is it ...
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Speed of EM Waves
We know that for electromagnetic waves, according to Maxwell's Theory
$$v=\frac{1}{\sqrt{\mu\epsilon}}$$
Now consider an opaque object like say Gold. It has a particular value of permittivity and ...
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Is $n=\sqrt{\mu_r\varepsilon_r}$ always true? even with complex value?
I have trouble deriving a supposedly "well-known" equation used in condensed matter physics:
$$n^2=\mu_r\varepsilon_r+\frac{i\mu_r\sigma}{\varepsilon_r\omega}$$
I'm sure that $n$ and $\sigma$...
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Do any of the color bands in a rainbow contain an electrical charge relative to clouds that might explain a photo of lightning striking a rainbow?
Caveat: While I am not a physicist myself, I am extremely interested in physical phenomena. I am well versed in electrical theory, and I am aware of the attraction between the bottoms of clouds and ...
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398
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Deriving the focal length of a graded index lens (GRIN)
I want to find a closed expression of the focal length of a graded index since I don't manage to find any on the internet. I already checked this out: Determining the focal length of a gradient index ...
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What are the physics behinde reflection and refraction of electromagnetic wave at a dialectric surface?
I have understood the most of the equations that lead to the Fresnel-Equations from electromagnetic waves and Maxwell equations. But not enough to understand what is happening. So I don't ask for an ...
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Decoherence of a laser beam via oil emulsion
This is sort of a followup to an earlier question that I posted regarding how to destroy the temporal and/or spatial coherence of a laser beam. It was suggested to me that I could use a rapidly ...
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Strength of electric field needed to observe noticeable effects on refraction in water
I was looking into the mechanism behind refraction and stumbled upon a Fermilab video explaining it has to do with the electric fields of the particles in the medium interacting interacting with the ...
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Analysis of the reflection in metal
In order to solve the reflexion in a material with a complex index the solution I've found on textbooks is to define $\hat{n}\cos{\phi}:=a+bi$ where $\hat{n}=n_r+n_ii$ is the complex index and then ...
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What does the wave created during refraction look like?
People always describe refraction as light stimulating the electrons in the glass, which create their own light, which interferes with the original wave. They always say “the math is too complex, but ...
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What does the wave look like during refraction?
For example, in this image,
It shows the wave contract and shorten the wavelength. Is this actually what light looks like in a denser medium or is it more like the wave is phase shifted back ...
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Is there a wave equation describing electromagnetic waves in materials?
Solutions to the usual wave equation for electromagnetic waves have the property that wave components of different wavelengths travel at the same phase speed $c$, so no dispersion occurs.
What I ...
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105
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Why is the refractive index $n$ linked to the wavevector $\hat{n}$?
Preamble: I'm studying light-light scattering in Effective QED but I notice that I don't remember a single thing from my EM/Optics courses so I decided to review some things.
Question: why is the ...
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Where can I find tables of the refractive index (real and complex part) or dielectric function as a function of frequency for different materials?
I need this information to do simulations for my master's thesis but I don't know if there is a bibliography or a repository on the internet with this information. They are simple materials, water, ...
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Why does the wave velocity of EM signals in a wire depend on the insulator's permittivity?
I'm in an electromagnetism class and struggling with a concept. The textbook derived several equations which state that the wave velocity of an electrical signal in a transmission line depends on the ...
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The operator calculation of Helmholtz equation?
I am reading the beam propagation method (BPM) in optical imaging paper. I find a paper solve the Helmholtz equation in the inhomogeneous media. The paper is:
Light propagation in graded-index optical ...
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491
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Variations in Refractive Index of Materials
It's quite a common fact that different types of glass have different refractive indices. Most sites I've found attribute these differences to variations in the 'density' of the glass, which is not ...
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Calculating the refractive index of water with the Ewald-Oseen formula
The Ewald-Oseen theorem gives the expression
$$n=\sqrt{1+\frac{i\sigma}{\epsilon_0\omega}}$$
for the refractive index of a material of conductivity $\sigma$ for an electromagnetic wave with angular ...
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How in Faraday rotator, changing magnetic field will change the refractive index of RCP and LCP?
Can anyone mathematically prove how in the faraday rotator, when we change the magnetic field direction, it will change the refractive index of Right circularly polarized (RCP) and Left circularly ...
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The difference between the equation of Permittivity and Permeability in a medium
I notice that the equations of Permittivity and Permeability in a linear medium are exactly opposite of each other. One is $$\mathbf{D} \equiv \varepsilon \mathbf{E}$$ while the other one is $$\mathbf{...
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A lens with a high permeability
In real life materials with high $\mu$ values are not realistic, so lenses are made with high $\epsilon$ materials. But what would be the impact of achieving the same refractive index by increasing $\...
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Why Analytic in the upper hald plane required for Kramers-Kronig relations?
I've been reviewing the contents after quite a while. Now, when I'm reading Kramers-Kronig relations, I see that everywhere it is stated that the complex function have to be analytic in the upper half ...
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214
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How can the speed of light in matter be measured?
Experiments such as Focault's measure speed of light in matter. Focault's experimental set-up is based on the idea that it takes more time for light to travel through matter, which will result in the ...
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Will changing the energy density of the vacuum alter its permitivity or permeability? [closed]
If one uses lasers or a variation of the Casimir effect to change the energy density of a region of free space, will this also change the permeability and the permittivity of this same region? Why or ...
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What happens to light as it enters a denser medium?
I am a first year undergrad student doing optometry (never done any physics before in my life :( ). I got a question asking what happens when light enters a denser medium. I was told that the ...
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What is the refractive index for dilute media?
For dilute media, which I assume is a weakly absorbing medium, I have seen the refractive index $n$ given as
$$n=\sqrt{\epsilon_r}+\frac{\text{Re}\{\tilde{\chi}_e\}}{2\sqrt{\epsilon_r}},$$
where $\...
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Appleton-Hartree Equation for different plasma wave phenomena
A lecturer referenced a plot of the refractive index squared vs the plasma frequency in relation to the Appleton Hartree equation.
In the plot it showed at different plasma frequencies the various ...
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Intuitive meaning of the permittivity and the permeability in Electromagnetism
I wonder what the correct way to intuitively understand the concepts of electrical permittivity and magnetic permeability would be.
The electric permittivity $\varepsilon$ of a medium is defined as a ...
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Are there materials that just change the speed of light?
Maxwell's equations in medium without charges read
\begin{align}
0&=\nabla\cdot D\,,\\
0&=\nabla\cdot B\,,\\
0&=\nabla\times E + \dot B\,,\\
0&=\nabla\times H - \dot D\,.
\end{align}
...
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Why it is necessary that phase of incident, reflected and refracted wave must equal at the interface of two medium?
1.Why it is necessary that phase of incident, reflected and refracted wave must equal at the interface of two medium to satisfy the boundary conditions at the interface?
2. According to boundary ...
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In anisotropic media, is there a speed of light tensor like there is a refractive index tensor?
Lets say we have an homogeneous anisotropic medium where $\tilde\mu_r=\tilde\epsilon_r$ so we don't have to worry about polarization effecting anything. As such, the refractive index can be simply ...
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$E$ field boundary condition and Snell`s law
So, for E field boundary condition, we know the vertical part of the incident field
$\varepsilon _{1}E_{1\perp } = \varepsilon _{2}E_{2\perp }$
and the tangential parts are same from both side.
That ...
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