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jewelers use a handheld magnifier that can be used as a quick approximate refractometer with some practice; they can tell the difference between glass and diamond this way. Precision refractometers can measure the refractive index accurately enough to identify the composition of transparent materials. Conversely, if the refractive index of a given type of ...


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This gets a little long to explain the situation. See the bottom for answer to your questions. Many textbooks do a bad job explaining the theory of blackbody radiation. In particular, often they assume perfectly reflecting cavity without explaining why they do so. It seems to be often just copied from textbook to textbook. I don't know who and where ...


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You haven't written the time average of $S$, you've written the spatial average of $S$, but that doesn't change your question. In calculating the average, you are interpreting $e(x)h(x)$ as a density. Poynting per meter. The Fourier transform converts this into spatial frequency space, so it becomes a density in spatial frequency space. That is, ...


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It holds but the Wikipedia, wannier orbitals and hamiltonian formalism unnecessarily blurs this very obvious fact. First assume that we have an action of Dirac fermions(this can also be non relativistic fermions as in your case it won't effect the argument) in $2+1$ flat space-time. $$S_F=\int d^3x\bar{\psi}\gamma^{\mu}i(\partial_\mu)\psi+m_0\bar{\psi}\psi$$...


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I'll rephrase comment by @LawnmowerMan as a new answer: The assumption that "classical model" had wrong was that it assumed frequency and energy of a photon are not connected. For example, it allowed photons that are both high-frequency and low-energy. However, quantum mechanism and real world experiments show that the energy and frequency of a ...


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Yes, you got a different result because you started by defining the direction of a positive field differently. If you reverse the defined directions of the reflected E-field and B-field (which you are free to do), then don't be surprised if your reflection coefficient reverses sign. This is perhaps more obvious to see at normal incidence, where the ...


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Confusion is caused by misleading notation. $E_p (\omega), H_p (\omega)$ is the first and the second case, are slightly different things. In the case of monochromatic wave - they are the whole electric and magnetic field. Because there is a wave with only one frequency I would drop the $\omega$ index, and denote them as $E, H$. And in the second case - it is ...


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Photons are particles and not to be confused with electromagnetic waves or wave packages. They do not interfere. EM waves do interfere. The EM interference pattern, more precisely$^*$ the value of $E^2$ at a position, gives the probability to detect a photon at that position. $^*$ This assumes the photon is detected by an electric dipole transition. For a ...


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You just raised a question about a very important topic, the distinction between interference and interaction. A lot of answers on this site mention interference in connection to the double slit experiment. And you see other phrases like "photons do not interact with each other". I think this needs a little clarification: Interference, you can see ...


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Ok since I have to give a full, valid answer to the question, that can stand on its own: The Peierls substitution does NOT work for time-dependent Vector potentials. The proof at Wikipedia is wrong, as it stands. Here is my proof: We start from the field operator representation of the Hamiltonian, for simplicity we assume that the Vector potential is spatial ...


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The waves associated with a single photon can interfere with each other (and contribute to producing an interference pattern). Different photons in a laser beam (all of which have the same wavelength and phase) can also interfere with each other (making holograms possible). Photons from an ordinary light source may have many different wavelengths and no ...


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Your question is correct, photons do not really interfere. The DSE taught at the high school level is a convenient theory and it also works well mathematically but 2 photons cancelling is a violation of conservation of energy. In university in quantum optics courses deeper explanations are provided. Think of 2 tsunamis one from Japan and the other from USA, ...


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Photons do interfere, there are places where you can see the classical interference patterns like in the double slit experiment (or every interferometer) and some places you can see quantum interference (e.g. Hong Ou Mandel experiment). The "sorting" of photons is an outcome of the lens in our eye, sorting photons coming from different directions ...


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Photons of different energy have different wavelengths. When they interfere with each other it isn't done in a linear fashion. Our sensors in our eyes can understand only a few frequencies of light.And the information of each wave is not lost in the collection of waves "polluting your eye".


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The classical version of blackbody radiation is given by the Rayleigh-Jeans law, and is described in detail in the corresponding Wikipedia article.


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The tangential field boundary conditions follow from the curl equations $$\vec \nabla\times\vec{E}=-\frac{\partial\vec{B}}{\partial t}$$ $$\vec \nabla\times\vec{H}=\vec{J}+\frac{\partial\vec{D}}{\partial t}.$$ The boundary conditions as you have written them assume linear media and no surface current at the interface. These boundary conditions are typically ...


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Let me add something to anna v's answer. The classical model of blackbody radiation is based on: an exact recasting of the Maxwell equations describing electromagnetic radiation in a cavity, which shows that this physical system can be described as an infinite set of classical harmonic oscillators (normal modes) whose frequencies start from zero and are not ...


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This link clearly shows the classical and quantum derivations Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated ...


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For an object (the green arrow) standing in front of the mirror, all the rays that impinge on the mirror send back at the same angle at which they impinge on it. These reflected rays seem to be coming from an object behind the mirror. It only seems further away (if you look in the mirror you see yourself twice the distance as you are standing in front of the ...


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As explained in detail in What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?, when complex field amplitudes like $E(\vec r,t) = h(\vec r)e^{-i\omega t}$ are presented, there is a broad convention that the physical field is obtained as its real part, $E_\mathrm{phys}(\vec r,t) = \mathrm{Re}\left[h(...


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I recall reading recently (do not remember where) that the mass equivalent of the photons in the universe $P_{ou}$ is about 90% due to the cosmic microwave radiation (CMR). However, the best values I found for calculating the mass equivalence of the radiation in the observable universe is based on three variables. (1) The mass of matter in the observable ...


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Very often in a wave propagation analysis, superscript '+' indicates the fields associated with the wave propagating in the positive direction and superscript '-' indicates the fields associated with the wave propagating in the negative direction. When calculating the impedance, you would take the ratio of the E and H fields for the wave travelling in one or ...


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I'm not really following your question well. It is well known that accelerating charges and non-stationary currents have a positive flux of Poynting vector over a closed surface around them. This is what we call electromagnetic radiation and it carries energy out of the system. If you have static charges, they produce no magnetic field. So the Poynting ...


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It's not that the light itself is converging behind the mirror, it's that if you extend the rays in a straight line following their new path after being bent in the lens, they will appear to come from a single point. This Khan Academy video explains virtual images well: https://www.youtube.com/watch?v=nrOg85VPQgw&vl=en


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Mass of the "observable" universe is about 10 to the power of 53. However, the answer of your question would be irrelevant, since what we have observed and measured is practically from the past. For example, the measured mass of a star in 1 billion light years from earth has added up to the calculation to get the "10 to the power of 53" ...


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First off, if the wire is "ideal" the answer is undefined. The ideal models provide no solution if you try to solve them. What actually happens is defined by the non-ideal aspects of the system. The magnetic field collapsing causes back-EMF, which induces a voltage on the wire. In small voltage cases, this ends up turning the wire into an ...


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This is the complex wave equation, $$ e^{\boldsymbol{i} z} = \cos z + \boldsymbol{i}\sin z $$ With $z=-\omega t$ Note, the imaginary unit $\boldsymbol{i}$ is missing in what you wrote. They are just saying that the solution being sought is a plane wave.


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Does this particle emit radiation? Yes. G. Smith explained this in detail in his reply. If so, where this energy comes from? The usual answer is that the spin of the particle is responsible for the deflection. If you dig a little deeper, a chain of events becomes visible. The important point here is to understand that electrons are not only charges with ...


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There will be a spark between the cut ends and the energy goes into the heat, light, and bang associated with the spark.


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The electric field of neighboring rays do not interfere. The electric field exists at a point. Every point in space has an electric field associated with it, that field characterized by direction and magnitude, or by components in "E-filed space" $E_x,\,E_y,\,E_z$. The arrows used to illustrate an electric field at a point have a serious ...


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Yes, it radiates. The energy of the radiation comes from the kinetic energy of the particle, which would decrease unless some kind of electric field causes the particle not to slow down. The force tending to slow down the particle is called “radiation reaction”. If the particle slows down, the trajectory is a spiral rather than a circle. For non-relativistic ...


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Firstly, if the objects are made of the same material but are different colours then presumably they are painted or dyed or otherwise surface-pigmented. If that is the case then, unless the paint is very thin, the absorption of IR radiation will depend more on the paint than on the underlying material. Different paints can have very different absorption (...


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Since the electrons arriving at the screen would tend to give it a negative charge which might repel or distort the arriving beam, there may be a need to connect it (as in your second diagram) to a circuit providing a potential which would minimize its affect on the beam.


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The refractive index is defined as the reduction of the phase velocity of light in a medium: $$ n = \frac{c}{v}. $$ In this sense light in a medium travels "slower" - because its velocity is smaller. One should however keep in mind that here we are talking about the phase velocity, which relates the length of the electromagentic wave with its ...


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But in this frame, a stationary charge on the earth does indeed accelerate, meaning that it should radiate. So why don't we observe that stationary charges in gravitational fields, like that of the earth, radiate electromagnetic radiation? Three observations: in the free-falling frame, the earth-bound charge is moving with almost constant acceleration. ...


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This is the answer I have given in The Large and the Small The paradox concerning the radiation of a charge in a gravitational field can be resolved using either classical electromagnetism or in quantum electrodynamics. The resolution in quantum electrodynamics is interesting because it shows directly that so-called “virtual” photons can be observable. The ...


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A lens deflects light rays, bringing them to a focus. A gravitational lens is typically a galaxy or cluster of galaxies. A galaxy typically has trillions of stars. The sun deflects light rays a little. See How the Sun Warps Starlight, or Gravitational deflection of light. A ray that skims its surface is deflected by about 1.8 arcsec. These rays would come to ...


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Somehow questions about inertia are related to these about a photon mass. The discussion about a photon mass can be conducted endlessly. In general: it is clear that a photon has no rest mass. Because it cannot be at rest. It can only exist after its emission until it is not absorbed. In between it moves at the speed of light. the emission of photons (...


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In 1856 with Rudolf Kohlrausch (1809–1858) he (Wilhelm Eduard Weber) demonstrated that the ratio of electrostatic to electromagnetic units produced a number that matched the value of the then known speed of light. This finding led to Maxwell's conjecture that light is an electromagnetic wave. This also led to Weber's development of his theory of ...


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The Compton scattering $\gamma e^- \to \gamma e^-$ can be regarded as an elastic process in the meaning that the total kinetic energy of the system is conserved (the final particles are the same as the initial ones). However to comprehend the interaction at both low energy limit $\omega \lt \lt m$ and high energy limit $\omega \gt \gt m$, you require the QFT ...


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Gamma rays and x-rays are both electromagnetic. Gamma rays have a shorter wavelength and more energetic photons. Each is identified by the range of wavelengths rather than the source.


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The speed of light was measured before Maxwell with the Fizeau-Foucault apparatus: 1848-1849 by Fizeau: $315000$ km/s 1862 by Foucault: $298000$ km/s 1872-1876 by Cornu: $300400$ km/s Around the same timer (1861-1862) Maxwell set up his equations for the electric and magnetic field. By solving these equations he could predict the existence of ...


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It was based on some experimental as well as theoretical measurements. Maxwell calculated the speed of his so called em waves for vacuum at that time using the formula derived from his equations $$ V^2 = \frac{1}{\mu \epsilon}$$ The value which he got from the above equation was $3 × 10^8 /s$ and this value was very close to the experimental measurement of ...


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Picture a wave on a string which is a 1D transverse wave. We see that though the waves move in 1D, the particles displace into an extra dimension. The wave moves in one direction but it oscillates perpendicular to this direction. In case of water ripples, they travel in 2D and their displacements are in 3D They oscillate up and down (one dimension) and ...


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In this link : Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of ...


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yes they do, and for the reasons you sketched out. In principle, it would be possible to construct a mirror "sail" which, when deployed near a star, could be used to propel a spacecraft via the photon reaction force. However, the reaction force is tiny and to generate useful accelerations, a sail many miles across would be required. Isaac Asimov ...


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$$\vec{H} = \frac{1}{c}(\hat{k}\times\vec{E}_0)e^{i(kx-\omega t)}$$ is incorrect. Perhaps you have $\vec{H}$ and $\vec{B}$ confused. The correct formulae are $$\vec{B} = \frac{1}{c}(\hat k\times\vec{E})$$ and $$\vec{H} = \frac{1}{\eta}(\hat k\times\vec{E})$$ where $\eta=\sqrt{\mu\mu_0/\epsilon\epsilon_0}$ is the wave impedance of the medium. With either one, ...


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An atom with an unpaired electron has a magnetic dipole moment. In a ferromagnetic material a significant fraction of the dipoles can be brought into alignment and will maintain that alignment in spite of thermal agitation. In a bar magnet, the alignment of the dipoles produces a magnetic field which is very similar to the field that would be produced by an ...


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The electromagnetism is pretty much wide field of knowledge and a lot of it goes well without the notion of any "spin". The spin concept is usually first invoked when one needs to explain ferromagnetism (the ability of some substances to retain a static magnetic field after the external magnetic field is removed). Unlike many ubiquitous ...


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