Nate Smith

Refraction

9 posts in this topic

I would like to understand why light bends as it passes through one medium to another (at an angle not perpendicular to the media border). Most explanations begin with the fact that light slows down in a denser medium (like traveling from air to glass). Often this process is described using the soldier analogy (a row of soldiers walks from solid ground to mud, and the soldiers on the mud move more slowly causing the row to bend).

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While this is a nice analogy, it doesn't explain why refraction happens. As soldiers walk onto the mud, they probably won't change direction, they will slow down. The column of soldiers to reach last will be ahead of the soldiers to reach first. After entering the mud, the soldiers will be moving in the same direction as before, but the front row will no longer be perpendicular the direction of travel. In other words, there won't be a path change, and the soldiers who entered the mud last will be ahead of those that entered first.

The only way that the row of soldiers would change direction would be if they were all connected in some way. This would cause rotation as one side of the rows moved faster than the other (as the link I included suggested demonstrating this phenomenon with students joined by meter sticks).

Another analogous example that made more sense was a water wave washing up on land (in a direction not perpendicular to the shore). As the wavefront approaches the shore, it will be at varying depths. The shallower part of the front moves slower than the deeper part (presumable because of friction). This causes the wave front to bend. I can understand why the bending occurs here though. Each water molecule is affected by those around it. As some water molecules are moving faster than others, there are pressure differences causing path changes.

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The main reason this puzzles me is because I don't really know what light is. Is it an array of individual beams or particles, independent of those around it (similar to the way I’ve characterized the soldiers). Is light more like water; is it more continuous, therefore each “piece” of light affects the light around it? Is there some analogy to “pressure” in light? Does gravity play a role?

Thanks for the help.

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My, very basic, understanding of the nature of light leads me to this rule of thumb: When an observed phenomenon involving light cannot be easily explained by considering light a particle, try considering it a wave.

As I've also heard, it's not always correct to consider light to be a particle and not a wave or vise versa but rather some kind of hybrid of both.

That said, consider light a wave and draw the same format drawing as the soldier analogy but use a set of waves emanating from a point outside the denser medium. You'll find in the new representation that, as the crest of a wave enters a new medium at a non-perpendicular angle, the form of the wave as it slows down will change uniformly. The reason that this is significant is that after this change the apparent point of origin for the waves that are now in the medium will seem to have shifted.

The reason I think the soldier analogy fails is because one is led to consider a soldier a single unit and not part of a rank of a parade. Think about what would happen if a rank of infantry, who are ordered to stay in rank, entered a field of mud that slowed each soldier by the same amount. If they we're to just slow down and not change direction they would no longer be in rank, but if they were to adjust their direction when they entered the mud at an angle they would be able to stay in rank with the others in like medium until the whole parade was in the mud.

This is purely a thought experiment and is how I have come to understand it but it doesn't say much about the physics of the situation.

take a look at my little drawing:

refraction.bmp

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Think about what a 'wave' of light would look like if it acted like soldiers just going into the mud without changing directions. It would look like a wave that had originated from a different point but was traveling as though it was still coming from the same point as the waves outside the medium. That would just not 'look right' because if the light had originated within the medium the point of origin would have to had sent out parts of the same crest at different times. It just "doesn't fit" mentally.

I really have no other way to approach this, maybe this didn't help. I don't know.

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Like others have said, it is the wave nature of light that you are overlooking. When you draw the example, you say that there is no reason for the soldiers to change direction when slowing down. This would mean that the front line of the soldiers is no longer parallel. But, because of the wave nature of light, the beam cannot be moving at different speeds and stay a wave. Thus, it must stay parallel. In order for the particles to be parallel with one another, they must curve as a whole.

I assume once you understand that particles must be parallel, you understand why they curve.

Hope this helps.

Zak

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Light is electro-magnetic radiation, which means it has both an electric field and a magnetic field associated with it (these fields are at right angles to the direction of propagation). As to what physically causes the slowing down of light, if that's what you're asking, it is the electrostatic properties of the material.

As to the bending part, the change in speed in the material is enough to explain the change of direction, though the concept takes work to grasp.

Imagine that the waves are like sea waves rolling from water into a more viscous liquid. The crests of such a wave will be a straight line entering a viscous material at an angle. The first parts of a particular crest to hit the viscous material will result in the a slowing of the wave, yet the crest will still be a line, now bent, at the point of interface between the two mediums. The molecules at the interface must oscillate at one speed. All of the wave crests will do this, and this is what changes the direction of the wave.

I drew a rough diagram here:

Refraction Diagram

The diagram shows the crests of a wave moving toward another medium. At t0, the wave crest is at A0 and B0. At t1, the crest of the wave is at A1 and B1. The A point moved much less than B point resulting in a bent wave front. After this the wave propagates perpendicularly to its front, as a sea wave would.

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The only way that the row of soldiers would change direction would be if they were all connected in some way. This would cause rotation as one side of the rows moved faster than the other (as the link I included suggested demonstrating this phenomenon with students joined by meter sticks).

A better analogy: picture a road with brush or high, thick grass on either side. Roll a large log down the road, at an angle to the direction of the road. Eventually one end of the log hits the brush and that end won't travel forward as easily as the the end of the log still on the road. This causes the log to rotate towards the brush as it travels forward. The direction of travel changes as the log moves from the road to the brush. (One can likewise imagine the log moving from the brush to the road, with the log again changing direction, but this time in the opposite direction.)

The main reason this puzzles me is because I don't really know what light is.

I see you like to ask the simple questions. :(

If you look through the history of physics or optics, you'll see many different theories of what light is. There is agreement of what is observed during specific classes of experiments, but the interpretation of those observations is under debate at the most fundamental level, with standard quantum theory and the Theory of Elementary Waves (TEW) positing very different answers. I don't have the final answer to that question, and really haven't studied quantum mechanics since college.

Is it an array of individual beams or particles, independent of those around it (similar to the way I’ve characterized the soldiers).
Yes and no. In some experiments, light behaves like a wave; in others, it acts like particles. It's a fascinating field, and if you're interested, I suggest spending time getting acquainted with some of the history.
Is light more like water; is it more continuous, therefore each “piece” of light affects the light around it?
A body of water consists of a collection of molecules that interact with each other through electromagnetic force. Very loosely speaking, you could think of a collection of small balls at rest in a grid, with springs connecting each ball to each immediate neighbor. If you push on one ball, the springs connected to it carry the energy from your push to the neighboring balls, which cause their neighbors to move, and so on. This movement propogates through the grid. That movement is a simple wave.

Or, tie a rope to a doorknob and grasp the other end. Snap your hand up and down quickly to send a pulse down the rope to the doorknob. That's another type of wave.

Waves of this kind are disturbances of some sort of medium. Without the medium, there is no wave. Sound waves are vibrations of air; remove the air, no more wave. Remove the rope or balls and springs, and there're no more waves.

For a while, scientists thought light, as a wave, must have its own medium, too. They called it the "ether" and theories abounded in the 19th century to describe it. Then an experiment around the turn of the century showed that there was no medium! That created a big problem for physics, and helped kick off a lot of the very odd theories of quantum physics to try to explain such observations. These waves didn't behave like any other waves we'd seen before.

Is there some analogy to “pressure” in light? Does gravity play a role?
Yes and it can. Light, in the form of photons (particles of light), travel from some source to a surface and can be reflected, transmitted, refracted or absorbed. In the case of reflection, the photons push against the surface enough to turn around and travel away from the surface. In doing so, they exert energy, pressure and momentum against the surface, which, following Newton's law, reacts to the collision.

Light can be affected by gravity. There's a phenomena called "gravitational lensing" in which the apparent position of stars is altered by the proximity of a very large astronomical mass. In effect, the light bends around these massive objects. However, it is a small effect, as it takes an extremely large object to create it.

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You've all given me a lot to think about. The most interesting thing I read was how light functions like waves very similar to water waves, but without a medium that it travels through. That's a hard one to get your head around. I'll look into that.

Thanks.

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The most interesting thing I read was how light functions like waves very similar to water waves, but without a medium that it travels through. That's a hard one to get your head around. I'll look into that.

Let us know what you find out.

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Nate, to understand refraction and why the "column of soldiers" is misleading and irrelevant you have to distinguish between material transport and the wave front's shape and orientation. Refraction is a change in direction of the wave front, i.e., a pattern of disturbance of the media, regardless of the motion of the underlying substance (water, photons, an elastic material, a gas, or anything else) which may or may not directly follow the refraction pattern, depending on the underlying dynamics which create the wave patterns.

The change in direction of the wavefront pattern is a simple consequence of change in wave velocity for any reason, not just at a boundary (for example, a gradually changing index of refraction for light, a changing depth of water, or a changing temperature of a gas). You can see the wave refraction consequences of change in velocity directly from the Huygens construction, as presented for example, in the introductory Vibrations and Waves by A. P. French.

An analysis of water waves helps to understand not only the basic idea of change of wavefront direction, but also the distinction between wave as a disturbance pattern vs. mass tranport and the physical cause of the wave pattern. You can see it either with a ripple tank in which two fluids of different density or viscosity are separated by a thin flexible membrane, or an analysis of shallow water waves of the type you see at the beach (which you may prefer :D)as they approach the shoreline at an angle to the contours of the bottom.

In the case of the shallow water waves, the particles of water are not approaching the beach as in a current; they are rotating in a near circular pattern following the shape of the surface waves, but returning underwater approximatley to the starting point. As the water becomes more shallow, there is more friction in the form of viscous drag near the bottom, and the waves slow down. The rest of the wave procedes at a relatively higher velocity, causing the wave front to turn, but there is no net mass transport towards the beach because the wave is not a current (although there may be an induced littoral current parallel to the beach due to incomplete refraction). The propogated wave energy, however, does change direction. See the classic (non-mathematical) Waves and Beaches by Willard Bascom.

In the ripple tank with two fluids separated by a membrane, the wave pattern progresses down the tank at an angle to the membrane, but the fluid does not flow through the membrane, which oscillates with the waves. Only the disturbance pattern changes direction due to change in velocity at the membrane.

For light, i.e., an electromagnetic wave, the refraction depends only the wave nature of the light and some boundary conditions across the interface. Light consists of collections of photons exhibiting certain wave patterns in the effect of their motion, but the refraction depends only on the wave aspect. See Jackson's Classical Electrodynamics or something similar for the standard explanation of refraction of plane electromagnetic waves. Feynman also tries to show with an elementary explanation roughly "how it works" behind the scenes in terms of probabilities for photons in a short section of his Lectures on Physics, Vol II, which may or may not help. To explain how photons behave requires quantum mechanics :(, and he gives a rough idea of the theory. Unlike refraction of water waves, the photons evidently also physically change direction.

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