I have a question about light. When light moves into a different medium, say into glass from air, we all know that light slows down and that different frequencies of light slow down more than others.
What I don’t understand is why higher energy light is slowed more than lower energy light? I would have assumed the opposite.
Because the higher frequency “hits” the interface more, well, frequently, offering more opportunities to lose energy.
Okay, I’ve got nothing.
Similar thoughts to me actually, something must be happening more often to slow higher frequency light down. What though?
It’s not true that the index of refraction of light always increases as wavelength decreases. (Higher index of refraction = slower speed of light.) In some materials, at certain frequencies, you can have what’s called anomalous dispersion, in which the index of refraction increases as wavelength increases. However, these situations generally occur when the light is near a resonant frequency of the electrons in the material; and since larger movements of electrons in the material cause absorption of light, the material is usually pretty opaque around these frequencies. Thus, in some sense, materials have “normal” dispersion because they’re transparent; they only have anomalous dispersion when they’re opaque.
Ignorance fought thank you, off to look that up.
The OP asks about the velocity of light in different media, and this answer mentions index of refraction. Is there a direct relationship between the two?
The ratio of the speed in vacuum (for light) to the speed inside the medium is the index of refraction. In general, the reference medium can be anything, but in the case of light is taken to be vacuum.
More simply,
n = c / v
n = refractive index
c = speed of light in vacuum
v = speed of light in the medium
Is it analogous to how high frequency sound is filtered out by apartment walls, but you can hear the bass thud through the walls a few units away?
Could be, could so why is the high frequency sound blocked whereas the lower frequency isn’t (or blocked as much)?
I don’t think so - at least I can’t think of any way these are analogous.
High frequency sound is more easily reflected, rather than transmitted, due to the shorter wavelength.
The key concepts are that (1) light is an electromagnetic wave, (2) materials are complex arrangements of charged particles, (3) charged particles react to (and can produce) electromagnetic waves. Taking these three facts together leads to a rich suite of phenomena, including the OP’s observation that blue light slows more than red light when passing through familiar transparent materials.
The electrons in a material may be fairly free to move around (like in a metal) or they may be bound tightly by their host molecules (like in an insulator). But the situation is far from black and white. Relatively free electrons will have collisions; some electrons could become free with the slightest bump; others resist disturbance with zeal. The details depend on the elements in question and on their chemical and physical arrangements. The electrons in a mixture of hydrogen and oxygen, for instance, behave very differently from the electrons in water.
Now, an electromagnetic (EM) wave (such as visible light) consists of electric and magnetic fields oscillating in time and moving through space. (For simplicity, we’ll ignore the magnetic component here.) When an EM wave passes through a material, the electrons in that material feel the oscillating push/pull of the wave’s electric field. Blue light, for example, presents to the electrons an electric field that oscillates back and forth at a frequency of 630 terahertz (630 trillion cycles per second).
A free and massless charged particle would react to the electric field like a pawn, being moved one way and then back again with no will of its own. The electrons in a material are neither free nor massless. Also, the ones that are bound will have frequencies at which they are happy to oscillate and frequencies at which they will react as a dog being dragged to the car for a visit to the vet.
A further complication is that the motion the incoming field is inducing implies necessarily that there are charged particles being accelerated. This is exactly how EM waves are produced in the first place! Thus, the incoming EM wave causes the charged particles to produce their own EM waves. One must add together all the waves present (the incoming one plus the zillions of little new ones) to see how the observable “total” wave behaves.
Now for the rich suite of phenomena…
Consider water. There are ten electrons in each molecule. (There is some redundance in bound states, so the number of differently behaving electrons is smaller.) There is also the molecule as a whole, something I have left out up to now. That is, the molecule has a physical arrangement (H-O-H, but bent like a boomerang) that acts like a spring. An external electric field can push and pull on the spring, and the spring (like the individual electrons) has a range of reaction and resistance to this forced oscillation, depending on the oscillation frequency.
So, even though H[sub]2[/sub]O looks simple, here’s the net result for waves of various frequencies passing through: plots for water.
The top plot is the one of interest here. It shows the index of refraction of water for a wide range of EM wave frequencies. (The index of refraction is the constant of proportionality between the speed of the wave in the medium to the speed of light in vacuum. So, n=2.0 means the wave travels twice as fast in vacuum as it does in the medium.) The x-axis of the plot covers an enormous range, from long-wave radio to high energy gamma rays. The tiny sliver in the middle that is delimited by dashed vertical lines indicates the range of visible light, from red to violet. Notice that the index of refraction increases slightly across this range. This increase is exactly the phenomenon in the OP. You can see that while an increase happens to occur through the visible region, other portions of the spectrum show decreases. The complex nature of the plot stems directly from the specifics of the electronic and atomic arrangements in a water molecule.
One can design materials to have certain desired properties at certain frequencies. This can be as simple as adding impurities (e.g., lead) to glass to increase the refractive index. This can be as complicated as making arrays of metallic panels to perfectly absorb a pesky range of microwaves.
[The bottom plot in the linked image, incidently, shows the absorption coefficient of water over the same range of frequencies. This is a measure of how opaque the material is at each frequency. Notice that the visible region happens to occur right where water has a narrow window of transparency. EM waves with frequencies a factor of 5 or 10 outside of visible won’t even penetrate a thin layer of water, so it would be hard to evolve eyes to work in anything other than the (inevitably named) visible range.]
It took 11 posts before someone could actually address the question, but what a nice job! Clear, direct, focused. Bravo, Pasta!
In order to keep it as simple as possible lets make the medium glass. Glass has transition energy levels in the ultraviolet and the energy of blue light is much closer to these levels than those of red light.
So given the Energy/Time Uncertainty principle, the amount of time a blue photon can undergo virtual absorption (a dressed state) is much longer than that of a red photon. Ergo blue light transits the medium at a higher speed.
Since the absorption is virtual and not real the photon maintains its original velocity vector and isn’t randomly scattered.
Oops, that should say “transits the medium at a lower speed.”
Pasta thank you very much for educating me that was an enlightening post.
I do not understand this bit at all can anyone help?
Here’s my possibly false but completely mechanical analogy.
Imagine an axle with two wheels which, for some reason, you’re fooling around with on a smooth surface like a parking lot.
If you roll it off the surface of the parking lot and onto the gravel edge the speed of the axle is reduced.
Now if you rolled it at an angle to the edge so that one wheel met the gravel before the other then the direction of the axle is going to change as the first wheel is slowed before the second wheel.
So you add another axle of a different length. Roll both axles off the edge at the same angle to the edge and the resulting paths of the axles will be different.
Because the longer one turned more sharply.
Smooth and gravel surfaces = different media.
Axle length = wavelength.
(Not original to me, read it in a Physics for Dummies book of some kind)
I think that explains why light bends not why some light is bent more than others.
That’s an awful general request. Could you be a little more specific?
I’m not sure to whom Ring could possibly be directing his “explanation”, as anyone who could understand what he is saying already knows the answer to the question at hand. (Ring presumably realizes this, so his post is a bit confusing to me in the present context.)
In any case, take another look at the figure linked above. Notice that the absoprtion spectrum has several spikes in it and that the index of refraction curve exhibits features at those same frequencies. This is not coincidence.
Consider the spring that is the H-O-H molecule. This spring has several fundamental vibrational modes, each with its own particular frequency (the mode’s resonant frequency). Light that is close to a resonant frequency of the material gives up its energy readily to the corresponding vibrational mode. In other words, light near resonant frequencies is more strongly absorbed that light far from these frequencies. But that’s just absoprtion. Index of refraction is a bit more complex. I’m on my way to dinner soon, so I’ll give a possibly unsatisfying answer here. Feel free to reply with a request for more depth.
Recall that the observable wave is the sum of the incoming wave plus the zillions of EM waves created by the perturbed charges in the material. If you treat the charges as a collection of damped oscillators (like car shocks, only less damped), and you perturb the system with your incoming wave, and you add up the resulting EM waves, you find the following feature: the resulting wave moves the slowest when its near a resonant frequency. (This is related to the following at-home phenomenon. Hold your shoe up by a long shoelace. This is a pendulum. Get it swinging a bit but then keep your hand still. You can see its resonant frequency. Now, “drive” the pendulum back and forth with your hand wayyyy slower than its resonant frequency. You’ll notice that the shoe stays more or less right beneath your hand. Now drive the pendulum right at the resonant frequency. Two things happen: The amplitude of the swing shoots way up as if by magic (that’s the shoe efficiently absorbing your input “wave”) and the shoe is always a quarter cycle behind your hand. If the shoe was emitting waves of its own, you can see that the resonant and non-resonant cases would lead to different sorts of constructive/destructive interference when you add all the waves together.)
Now, a completely separate way to approach the problem is to think of the incoming light as a collection of photons. This treatment requires quantum field theory (whereas the above classical approach does not.) Two key concepts from QFT are needed: (1) the energy of your photon can change as long as it changes for such a short amount of time that you can’t measure the change (Heisenberg uncertainty principle), and (2) anything that can happen, does, just with varying probabilities.
Invoking (2), a photon that is near an absorption frequency can be thought of as simultaneously being absorbed and not being absorbed. However, it can only be absorbed if it is at the absorption frequency, which it isn’t. Invoking (1), we just say that the photon has a different energy for a little while. The closer the real photon is to the resonant frequency, the longer it can “be” at that frequency without breaking any rules. (You can see why the word “virtual” might appear.) In short, a closer-to-resonance photon spends more of its time virtually (but not really) absorbed and thus takes longer to get through the material. Hence, the index of refraction peaks when absorption peaks.
Ring further introduced the fact that glass happens to have lots of absoprtion in the UV. Blue light, being closer to the UV than red, thus has the higher index of refraction (the observation in the OP).
But, the QFT approach is not necessary, so feel free to think solely in terms of classical waves.
