I have been teaching refraction for years at a beginner level. At the interface when light strikes a different medium, its speed changes and it refracts. The more the speed changes the more it will bend. A simple rule that I use is that if the light is moving from high density to low density (such as light moving from water to air), the ray will bend away from the normal and when the ray moves from low to high density (such as light travelling from air to glass) it will bend toward the normal.
However, I also know that glass can disappear in vegetable oil because their refractive indexes are the same. Glass and vegetable have nowhere near the same density.
Refractive index is clearly independent of density.
What is it about the material that makes light slow down in it?
Most often, it’s due mostly to the dielectric constant of the material, though the diamagnetic constant is also involved and can sometimes be relevant. Basically, it’s the tendency of atoms in the material to be distorted, with the electrons moving a bit one way and the nuclei the other, in response to an electric field.
Density isn’t completely irrelevant, but you need a significant difference in densities (like from air to water or glass, about three orders of magnitude) for that to be the dominant consideration. Transparent solids and liquids mostly only vary by about one order of magnitude in density, which doesn’t matter much.
Pyrex Glass “disappears” in vegetable oil not only because they have the same refractive index, but because they have very nearly the same dispersion. That is, they have very nearly the same refractive index over a large range of wavelengths.
If, on the other hand, you have two materials that have the same refractive index at one wavelength, but the refractive indices vary significantly at other wavelengths, then you have the makings of a Christiansen Filter, so named after the guy who discovered the effect, Christian Christiansen (really!).
If, for instance, you took that Pyrex, shattered it into fragments, and immersed it instead into a mixture of methyl salicylate and methanol, varying the relative proportions so that you matcherd the index at one wavelength, you’d find that you had a pretty god transmitter at that wavelength, but the other ones get scattered. So the filter appears colored and almost transparent. You can vary that wavelength by playing with the proportions of methanol to methyl salicylate, or by changing the temperature.
**Chronos[/B[ has already talked about the relationship between density and index – there often is a rough correlation, but not enough to say if refractive indices would be identical. Nonetheless, lithium compounds tend to have really low refractive indices, and heavier minerals or glasses do tend to have higher indices. but it doesn’t necessarily apply to a solid and a liquid having the same density. Nor, for that matter, do all liquids of the same density have the same refractive index. And their dispersions can vary all over the map – Methyl Salicylate has a huge dispersion compared to methanol. You can’t make a blanket statement about one having a higher refractyive index than the other, because it depends upon which wavelength you’re talking about.
I think the rule of thumb is density times dielectric constant. Or something like that.
As this is GQ, light does not “slow down”.
The refractive index is actually an observation of another effect, where the entire electron structure interacts with the light and the result of that interaction results in what is observed as diffraction.
While it is helpful for some problems to consider light as a particle or a beam in this case the more accurate model is a wave in this case.
While still a simplified analogy with flaws, consider a lens. You can think of light as going through all possible paths in that lens and the transmitted light as being the product of those paths, but it is typically more accurate to consider that the wave front is interacting in a part of the of it’s cycle in that angle, resulting in a “phase shift” although that term is overloaded and prone to differing opinions.
While still flawed it may be useful to consider that this phase velocity is related to the electromagnetic wave are effected by the same electromagnetic elements of the subsistence interacting with each other.
The popular description of light being slowed or stopped is a useful short hand, but microscopically for this to happen the light has ceased to be light.
This isn’t very useful for practical applications, but as you were asking about the fundamentals, the speed of the electromagnetic propagation is the important part.
The longitudinal wave propagation speed through a spring like a slinky may be another way to visualize this. How the wave propagation is related to the number of coils the spring has. Then consider the reference frame of an electron, being excited by an electromagnetic wave. Your interaction with neighboring particles will not be at C, and that can also be considered as a similar (still flawed) analogy.
Personally I find this way of thinking far more useful as it helps conceptualize effects diffraction and/or Airy disks witch become problematic with the the slowed partial type of analogy.
In a preemptive attempt to avoid responses that may detract from the OP’s intent, I am still talking about the classical model, but the “interaction of all of the atoms” analogy solves some problems that the long path and or absorb/re-emit descriptions have around a lack of phase change or stochastic effect.
One photon, two slits; or the theological implications of the polariton was not my intent.
But, the differences in air densities cause mirages yet these densities cannot be different by an order of magnitude.
Thanks for all responses. This seems to be one of those common phenomena found in introductory science texts that are caused by factors way too complex for that level of student to truly understand.
Air temperature, as in mirages, causes only a very small difference in index of refraction (after all, both hot and cold air are usually approximated as having an index of 1). It’s just that, in a mirage, you’ve got an extremely thick “lens”, so even very small differences have a chance to add up.
How thick of a lens do you think that would be? It seems to me that the changes in temperature needed for a mirage occur in a few centimeters of air above the road.
But you’re not looking through just a few centimeters. You’re looking through tens of meters or more.
It’s not the height, it’s the length. There’s a looong stretch of air you are looking thru. A tiny change added up over a half mile comes to a pretty big change.
There are two ways to look at this, depending on whether you want to consider light a wave or a particle.
If a particle: the photons coming in are generally absorbed and re-emitted by the atoms in the material. That process takes a nonzero amount of time, so it’s more or less as if the photons were taking potty breaks as they traveled down the highway. So the light slows down. The more closely spaced the atoms are (higher density) or the more effective each atom is at absorbing photons (polarizability), the more potty breaks they take and the slower the light goes.
If a wave: the oscillating electric field induces an oscillating polarization in the atoms (the electron get shoved in one direction, the nuclei in the opposite). The polarization takes time, sort of an electrical “inertia” effect, so the wave slows down. It’s roughly as if you had a wiggly wave traveling down a string and it hit a section where the string was thicker and heavier. The greater the polarizability of the material, roughly, meaning the more closely spaced the atoms (density) and the more electrons per atom and size of the atom et cetera the “heavier” the string is getting and the more the light slows down.
In either case you can see how both the number density (e.g. atoms per cubic centimeter) and the nature of the material (type of atom) matter.
There are giant amounts of simplification in the above, so this is just a 40,000 foot view sketch which is in the right conceptual direction but parseable by the average high-school mind, I think.
A good place to start for a more quantitative view is the Clausius-Mossoti relationship.
To add to this.
If you are talking about an Inferior mirage like the type you see on hot asphalt it isn’t a case of a single surface refraction like in a lens or when looking into a lake.
Using the particle view; Light that is traveling downward into less optically dense air curves to your the point where it is traveling your direction. This density change happens over a gradient and is why the image appears flipped, as the light from the top of the object travels through a broader change in density.
Think of the movement of a curve ball vs a fast ball, that spin gradually changes the direction vs. diffraction in glass or water which will more closely behavior like an 8 ball hitting the bumper on a pool table.
The main point being that the light that appears to be coming from the actual object travels through a more uniformly dense section of hair, when light rays that would have hit the ground in front of you are passing through a more pronounced pressure gradient.
It is a good example of Fermat’s principle of least time. You can consider the light is curving to find the fastest, shortest path for the phase front.
This is the same reason you don’t see an infinite number of images in a mirror, due to the changing density the “fastest” path in this gradient is a curved line.