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Sorry, the speed of propagation is exactly c/n, where n is the index of refraction. The angle of deflection (the refraction from which the index gets its name) arises because of (a) the difference in propagation speeds, and (b) the angle of incidence on the boundary of the medium.
And "all light moves at the same speed in a medium" is not close enough for a beginner, since that statement directly predicts the nonexistence of rainbows. Without n(lambda), you would not get dispersion.
I don't need to do a Web search for bremsstrahlung. I have been a practicing particle physicist for 20 years, and brem is one of the real annoyances when trying to reconstruct electron trajectories. The brem photons tend to be fairly low energy (MeV or less), so they aren't well reconstructed in calorimeters, but they can change the electron momenta non-trivially.
"They had an open-pool reactor going -- with not much between us and the pool but a don't-walk-past-here barrier"
Man, those were the days. That is a totally awesome idea (can you tell I'm a native Californian?), and the safety folks would have their knickers in such a twist now :-(
:-P No worries. I've done the same thing to experts in some of my comments.
I'm not sure you're remembering it differently. In almost every physics class, refraction is shown with a nice ideal optical ray, and a parameter n that looks like a constant. Then they pull out the plastic prism to make a rainbow. But almost never does the teacher point out that you can't make a rainbow if n is the same for all wavelengths! It's just impossible. So students are left with a fairly basic misunderstanding.
By the way, I think you meant Cherenkov radiation (see my self-reply, below) in your comment, not brem. Bremsstrahlung ("braking radiation") happens when an electron is deflected or passing near an atom in a material; the acceleration of the charged particle causes it to radiate, just like classical Maxwell's equations predict. The German name comes from the fact that electrons hitting material slow down ("brake") due to energy loss, including brem.
You did miss something. In vacuum, all electromagnetic radiation (radio, microwaves, infrared, visible light, UV, X-rays, gamma rays) travels at exactly the same speed, c.
In a transparent medium, the speed of propagation is reduced by the index of refraction n, which is why light rays are bent passing into or out of such a medium (water, glass, diamond, fused quartz, whatever). In water, for example, light is travelling at just 0.75c (since n = 1.33).
Typically (despite what you learned in your high school physics class), the index of refraction varies with wavelength. so different wavelengths will travel at different velocities through that medium. It also means that different wavelengths are bent at different angles. I leave it as an exercise to the reader to name a commonly observed consequence of a wavelength-dependent refractive index.
The fact that the index of refraction reduces the speed of light in a material has a very interesting consequence. Charged particles (like the electrons from radioactive beta decay) can travel at any speed less than c, depending on their mass and energy.
If a particle goes into a material where c/n is lower than the particle's own speed, it will produce an electromagnetic "shock wave," called Cherenkov radiation: This is a cone of light coming off the particle's trajectory, with the angle of the cone dependent on how much faster than c/n the particle is moving.
The radiation spectrum of Cherenkov light tends to be blue, violet, and UV. The glow you see (below) from radioactive materials stored underwater, such as the fuel rods at a nuclear power plant, is Cherenkov radiation from the beta decays.
The answer isn't relative. One of the basic points in special (and general) relativity is that the laws of physics are absolute -- the same in every reference frame, regardless of the motion of the observer.
One of those laws is the constancy of the speed of light in vacuum. It does not matter how fast you are going, you will always measure light to travel at the same speed, c = 299 792 458 m/s, no more and no less. You wlll see the wavelength to be different than some other observer (the Doppler effect), but not the speed.
Regarding your comment about quantum theory, can you provide a reference? Are you thinking of the superluminal phase-velocity experiments from a few years ago?
Thanks for the link, Rick. I notice that most of the "scientific" claims are either unsubstantiated hypotheses, or unreplicated one-off experiments.
There have been some good experimental results with tunnelling through dielectrics which show "apparent FTL" propagation -- the phase velocities of particular frequency components can be computed to have travelled superluminally, but the group velocity (which is the speed at which energy and/or information are carried) remains subluminal, usually significantly so.
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Posted:Aug 12, 2010
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