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378

The problem Lasers do all sorts of cool things in research and in applications, and there are many good reasons for it, including their coherence, frequency stability, and controllability, but for some applications, the thing that really matters is raw power. As a simple example, it had long been understood that if the intensity of light gets high enough, ...


117

You have created a rather poor pinhole camera (camera obscura). You can see an "image" of the sky, a green space (trees) and even a reddish brown blur that is your driveway. This is not diffraction or refraction - it's geometrical (classical) optics. Because the hole is pretty big, you see a very blurry image. But basically, the light from the sky falling ...


39

It does create the rainbow, but it is almost impossible to notice. When light direction is changed on the glass-air interface - there is always a dispersion : light with different wavelength will refract at different angle and thus create rainbow. The issue is that when light hits second glass-air interface - incidence angle is opposite, and dispersion ...


30

like even when light gets on the moon why does the space appears dark from the moon? For the same reason it appears dark from the Earth (when flying at an altitude of 80,000 feet or so): Image credit: View from the SR-71 Blackbird. The fact is, we can't 'see space' from the Earth's surface during the day because the atmosphere is 'in the way'- the ...


30

I think that this question is why sound waves are non-dispersive whereas gravity waves on the surface of water are and also depend on the depth of the water. In fact if the depth of the water is less than about half a wavelength, the speed of the gravity waves is $\sqrt{gd}$ and not dependent on the wavelength of the waves. The speed of gravity waves ...


28

Lorentz came with a nice model for light matter interaction that describes dispersion quite effectively. If we assume that an electron oscillates around some equilibrium position and is driven by an external electric field $\mathbf{E}$ (i.e., light), its movement can be described by the equation $$ m\frac{\mathrm{d}^2\mathbf{x}}{\mathrm{d}t^2}+m\gamma\frac{\...


24

They do. It's called chromatic aberration - each different frequency has a slightly different focus point, blurring the image by different amounts for the different colors. Modern lenses of high quality have multiple elements added specifically to address the issue of chromatic aberration. What happens with flat glass isn't chromatic aberration - that's an ...


20

The dynamical origins of the two are extremely different. Surface waves in water are gravity waves, which means that the restoring force trying to bring peaks and troughs back to the mean height is gravity. Peaks are higher than the surrounding water and tend to fall, while troughs are lower and tend to fill up with the water from the peaks on either side. (...


18

As you have probably noticed, the moon is tidally locked with the earth so that we always see the same side. You can look up in the sky and watch sunlight move across the moon's face. From the surface of the moon this change in illumination would look just like the day/night cycle on Earth ... except that it's roughly a month long. Until the advent of radar ...


16

Dispersion of sound in air, with constant temperature and pressure, is very slight, increasing for very short wavelengths, and for very loud noises. Why? Because the rapid sequence of weak compression/decompression steps as the sound propagates are adiabatic, or energy-conserving, for the normal ranges of sound. This leaves the local pressure, temperature ...


15

The simple explanation given in Hewitt's Conceptual Physics is that atoms in condensed matter have a high-frequency resonance, and the index of refraction for most substances is strongest at the blue end of the spectrum because that's the high-freqency end, which is closest to the resonance. The following is my attempt to flesh this out with a little more ...


10

In non-relativistic systems both $E\sim k$ and $E\sim k^2$ are possible. Quadratic dispersion relations occur if $\langle 0|[Q_i,Q_j]|\rangle\neq 0$ for some of the generators. This occurs in a ferromagnet because rotational invariance is broken and $J_z$ has an expectation value. In terms of effective lagrangians the difference between ferromagnets and ...


10

As an addendum to @EmilioPisanty’s excellent review, I’d just like to mention one more application of CPA lasers, which may be overlooked from a theorist’s perspective: Ultrafast Spectroscopy Sometimes lower-order nonlinear processes like second-harmonic generation are enough; you just need them done efficiently for practical purposes. Lasers based on ...


9

What you want to do is change the wave equation into a Klein-Gordon equation: $$\frac {1}{c^2} \frac{\partial^2 \psi}{\partial t^2} - \nabla^2 \psi + \alpha^2 \psi = 0,$$ where $\alpha$ is a constant of appropriate dimension and usually (in quantum theory) given by $$\alpha=\frac {m c}{\hbar}.$$ Inserting an ansatz of the form $$\psi=e^{i(kx-\omega t)...


9

Short Intro The nonlinear term or steepening term, $\left( \mathbf{V} \cdot \nabla \right) \mathbf{V}$, determines the rate of steepening of a wave. This can be balanced/offset by loss terms like dispersion (e.g., $\propto \ \beta \ \partial_{x}^{3} v$), diffusion, viscosity (e.g., $\propto \ \nu \ \partial_{x}^{2} v$), resistivity, friction (e.g., $\...


9

Electromagnetic radiation in a medium propagates according to the law $$ \mathbf E,\mathbf B \propto e^{\imath(\pm k_xx-\omega t)} $$ where $$ k_x^2 = \frac{n^2\omega^2}{c^2}\;. $$ The refractive index $n$ can also be complex, in which case its imaginary part describes the absorption of the EM wave in the medium. But the oscillating part is in any case $$ \...


9

Sean E. Lake's answer is right: convex lenses disperse light like prisms and that effect is known as chromatic aberration - which is easily noticeably by zooming in in the corners of photographs taken with cheap cameras. I would add to his answer the reasons why usual convex lenses disperse light much less than a prisma does. For example, it's difficult to ...


8

The speed of sound is constant in the same sense that the mass of an object is constant. In the typical audible range, at frequencies below, like, $100\:\mathrm{kHz}$ and sound pressures much less than atmospheric pressure, the behaviour of air is very well described by a simple linear wave equation that's purely second order in both space and time. As a ...


8

The term dispersion refers to the speed of light in a material having a dependence on frequency (or equivalently wavelength). The refraction angle's dependence on frequency is caused by the material dispersion, not the other way around. In all materials the refractive index will have dispersion but it's often the case that certain materials in certain ...


8

Take a look at Griffiths Introduction to Electrodynamics, particularly the section called "The Frequency Dependence of Permittivity". Dispersion can arise from the constraints, or bound nature, of the constituent particles in a given medium. For the example of optical dispersion in a dielectric medium, we could picture the electrons as bound, damped ...


7

An easy way to make this intuitively plausible is by remarking that the Schroedinger equation in the absence of a potential is as follows $${\partial\over\partial t}\Psi = \nabla^2\Psi$$ up to constants, which is the heat equation if we ignore the fact that the omitted constants are complex numbers rather than real and of the right sign. If you consider ...


7

Suppose you have an infinite plane wave. To find the momentum of this wave you Fourier transform it. Because it's an infinite wave the Fourier transform is a delta function and the wave has a well defined single value for the momentum. Now take a wave packet i.e. the same infinite plane wave but now multipled by some envelope function. When you Fourier ...


7

I will hand wave here, looking at the problem a photon at a time. We know from the double slit experiment that even individual photons impinging on the double slit geometry display an interference pattern, characteristic of the frequency/energy of the photon and the geometry of the slits. One can think of a crystal as a very large number of three ...


7

The speed of sound depends primarily on the properties of the medium: density (atomic weight), modulus (for solids), and adiabatic index (for gases). This means that it changes with composition of air (which is one reason why you sound funny when you speak after inhaling helium) and for a given gas, with temperature (see http://www.sengpielaudio.com/...


7

It is indeed possible. This was a famous experiment by Isaac Newton (published in 1672). Place a lens of focal length $f$ a distance $2f$ from the first prism. Add a second identical prism $2f$ past the lens and rotate it round until white light emerges. The lens is required to bring the rays back together. It creates an image of the exit of prism one on ...


7

Dispersion in waves arises from both material property variation with frequency and from the geometry of the fields in question. That wave dispersion will arise from material property variation is obvious. But wave geometry and boundary conditions also matter. Simple example: a conductive waveguide with rectangular cross-section with sidelengths $a$ and $b$...


7

Electromagnetic waves include visible light, radio waves, X-rays, and so on. What distinguishes these different bands of light is their frequency (or wavelength). But what they all have in common is that they travel at the same speed in vacuum. The reason for qualifying 'in vacuum' is because EM waves of different frequencies often propagate at different ...


7

In fact your statement is not quite right: air does disperse light - its refractive index does depend on frequency, albeit very weakly. If you replace "air" with "vacuum" in your question, then the statement you are asking about is a correct one. Dispersion arises from the interaction of light (an electromagnetic field) with the electrical charge present in ...


7

The fundamental energy-momentum relation in special relativity is $E^2=p^2+m^2$ (let’s ignore factors of $c$, since they will factor out in the end — that is, let’s work in natural units). Taking the derivative with respect to $p$ on both sides gives $$2E\frac{\partial E}{\partial p}=2p,$$ since $m$ is a constant. Thus, $$\frac{\partial E}{\partial p}=\...


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