Refraction - The lingering question

[Burningmace]

A few years ago when I was doing my Physics A-Level, me and a few others took part in a competition in which we had to perform a short play that educated a group of non-scientists about a something to do with physics. We chose refraction and showed how a laser bent in a fish tank at different angles. At the end of the play, the panel asked us questions. Being the person in the group that knew most about refraction, I took the lead on answering them. One of the questions completely stumped us and even our teacher. I think the exact question was the following:

Why does this happen? I get the maths, but I can just picture all these little photons coming up to the new type of material, whipping out their calculators, working out the angle and taking aim.

The best answer I've had from anyone I've asked has been a rather vague (and possibly blabbering) "I think it's got something to do with how the constituents of light interact at a quantum level".

So, anyone got an answer for me?

 

[mgb_phys]

It takes the path that minimises the total time - Fermat's theorem.
You could say it takes all possible paths but we exist in the universe where it found the shortest one.

 

[Burningmace]

I don't understand. Refraction doesn't minimise the total time to traverse the material, because that would mean that if I put two pieces of 5x10x50cm plastic with different refractive indices next to each other and shined a laser through it at 20 degrees off the surface, it should always attempt to directly through the 5mm direction. I attached a diagram to show what I mean. The blue and green lines represent the shortest distance possible across the material as the laser crosses between each material.

I read up on Fermat's principle, and I still don't understand.

 

[Danger]

This kind of controversy is precisely why I based my play upon the relative friction coefficients of lubricated vs. non-lubricated condoms.
The marks weren't great, but it's astounding how many non-science spectators attended the opening.

 

[Burningmace]

Hehe. Still though, anyone got an answer for me?

 

[Doc Al]

I don't understand. Refraction doesn't minimise the total time to traverse the material

What's minimized is the travel time between two points.

 

[Burningmace]

I sort of understand, but it still makes no sense. What defines these points? As light travels in a vacuum, it can't be atoms.I'm trying to think of it from the photon's point of view. As far as I can see, the difference between an opaque and a translucent material is that an opaque material has enough particles per square nanometer (unit is not important) to absorb and re-emit the photon enough times for it to become too low-energy to be in the visible spectrum, whereas a translucent material is less "dense" (I use that in a rough sense - the particles per square nanometer thing again) and doesn't absorb/emit the photon enough times to significantly lower its energy. Though, if this were true I could get red light from blue light using a piece of plastic (less energy -> lower frequency due to E=hf -> different colour light.

What happens to the photons as they navigate through a material? What happens to the photons when they move to a new material with a different refractive index? All the photon comes into contact within a substance is free space and the odd neutron/proton - if it's lucky it'll hit an electron. Why does a change in the composition of a substance alter the direction of light?

 

[jtbell]

It looks like you're visualizing photons as tiny localized pellets which follow trajectories through space like classical particles. They're not.

 

[Vanadium 50]

Why bring photons in it at all? This is a purely classical wave phenomenon.

 

[ZapperZ]

I sort of understand, but it still makes no sense. What defines these points? As light travels in a vacuum, it can't be atoms.I'm trying to think of it from the photon's point of view. As far as I can see, the difference between an opaque and a translucent material is that an opaque material has enough particles per square nanometer (unit is not important) to absorb and re-emit the photon enough times for it to become too low-energy to be in the visible spectrum, whereas a translucent material is less "dense" (I use that in a rough sense - the particles per square nanometer thing again) and doesn't absorb/emit the photon enough times to significantly lower its energy. Though, if this were true I could get red light from blue light using a piece of plastic (less energy -> lower frequency due to E=hf -> different colour light.

What happens to the photons as they navigate through a material? What happens to the photons when they move to a new material with a different refractive index? All the photon comes into contact within a substance is free space and the odd neutron/proton - if it's lucky it'll hit an electron. Why does a change in the composition of a substance alter the direction of light?

Please read our FAQ in the General Physics forum on the topic of light moving "slower" in a medium. The same explanation applies here.

Zz.

 

[Dale]

Adding to what jtbell and Vanadium50 said, not only are photons not tiny pellets, but refraction can and should be understood in terms of the wave equation. Quantum concepts like "photons" only get in the way.

Refraction is a property of all waves (water waves, sound waves, light waves, mechanical waves, etc.) whenever they go from a region with one speed of propagation to a region with a different speed. It falls out of solutions to the wave equation naturally without the need for any part of the wave to have any non-local information.

 

[flatmaster]

Fermat's theorem never really made that much sense to me. Conceptually, I like to use the example of the truck in the mud. If a truck is driving from mud (n=1.333) onto blacktop (n=1), if it approaches with the left tire first, that tire will gain traction and cause the truck to turn right. Likewise, You can think of the ray of light as having some width. If the left side exits the medium with the lower index of refraction first, that side will "speed up" and cause the ray to refract to the right. Conceptually, it's a pretty bad analogy, but it would have worked for that audience.

 

[DeShark]

Why does this happen? I get the maths, but I can just picture all these little photons coming up to the new type of material, whipping out their calculators, working out the angle and taking aim.

Nobody knows WHY this happens. That's not the place of physics. You'll need to look to other places (a bible, a torah, a belief in mother nature, or question rather "why not?"). What physics can do is give you a picture which will give a good description of what happens and sometimes will explain why in terms of other things that we don't know why.

It depends on which theory you want to use.

If you use Fermat's principle, then we look at the place that the light started out at and look at the place it finished. Then we see, every time, that the path which was taken by the photon is the one path out of the infinite number of paths which takes the least time. It's the same for electrons, except the quantity which is minimised is known as the "action", not the time.

If you want a way of knowing the path according to the Huygen's principle (each point on a wavefront acts as an independant source, then you say that as the wavefront of the light moves across the boundary, each point acts as a new source of light. Since the light travels slower, then the wave is refracted. http://www.walter-fendt.de/ph14e/huygenspr.htm Click "next step" a couple of times to follow it through.

If you want to use classical optics, then you can see that the wave interferes with itself, due to the reduced speed in the new medium. I can't find a picture to explain what I'm on about and it's quite difficult for me to describe (This generally means I don't understand it). I have a good book on optics which would do the job, but I don't have it to hand right now (it's in another country).

If you'd like to use quantum mechanics then all we can talk about is the probability of finding the photon at a given point. It turns out that the probability of finding the photon at a given point can be found using the path integral formulation of quantum mechanics, but no-one knows why. This is usually described mathematically. To describe it fully without mathematics would require a master of quantum mechanics. But don't worry, you can find one at http://vega.org.uk/video/subseries/8 The first two lectures will fully answer your question in a quantum mechanical way, much better than I could do here.

Hope you don't get bored reading my post and I hope it helps you out.