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This was explained to me many years ago, by a physics teacher, with the following analogy:

"If someone on the beach wants to reach someone else that is in the water, they will try to travel as much as they can on the beach and as little as possible on the water, because this way they will get there faster."

I'm paraphrasing of course, but this is as accurate as I recall it.
This explanation makes no sense to me. Was he telling me the light knows where it is going? It wants to get there faster? It chooses a different direction?
(No need to answer these questions, this was just me trying to understand the analogy.)

My attempts to clarify the issue were without success and many years later I still don't know.

Why does light change direction when it travels through glass?

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Yes, the simple (but true) explanation is that light known where to go. This is known as Fermat's principle. The deeper explanation of this peculiar fact is given by quantum theory. See my answer here: physics.stackexchange.com/q/2041 –  Marek Aug 17 '11 at 6:53
Aha, I only now noticed that these questions only interest you marginally. If you want a down-to-earth explanation of the fact, it (and great deal more) can be e.g. easily derived from Maxwell's equations of a plane-wave interacting with a boundary. But this won't give you the fundamental understanding that only comes from the path integral formulation of quantum theory. –  Marek Aug 17 '11 at 6:57
this reminds me of v.cx/2010/04/feynman-brazil-education –  karlzt Aug 17 '11 at 16:26
Following some of the links suggested by the answers below (thanks everyone), I found a very similar explanation (en.wikipedia.org/wiki/Snell%27s_law): "In a classic analogy, the area of lower refractive index is replaced by a beach, the area of higher refractive index by the sea, and the fastest way for a rescuer on the beach to get to a drowning person in the sea is to run along a path that follows Snell's law." –  Paulo Pinto Aug 19 '11 at 23:31
Related: physics.stackexchange.com/q/466/2451 –  Qmechanic Feb 20 '14 at 0:17

7 Answers 7

The teacher was trying to explain Fermat principle which is one of the simplest variatinonal (least action) principles of classical physics. And your question seems to express to a common frustration over the seemingly "teleological" property of all variational principles: how does the (partilce, wave, ray ...) "know" in advance which path to follow? Wikipedia article on the principle of least action specifically addresses this frustration (but does not give valid references, unfortunately).

The laws of propagation are local in time and space but it is sometimes easier to deduce their outcomes using non-local mathmatical constructions such as a Fermat principle. The teacher gave a great analogy to explain the principle but should not expect toget a step-by-step picture out of it.

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Light is an electromagnetic wave. electric field and magnetic field oscillations are perpendicular to each other. They keep on generating each other. The direction of propagation of an EM wave is given by the Poynting Vector which is a vector in a direction perpendicular to both the directions of vibration of electric field as well as magnetic field. Now when light goes from one medium to another, say, from air to glass, what happens is that the E- field polarizes the atoms of glass. Now as the E field is oscillating the polarizing effect is also oscilating , that is , it changes direction of induced dipole moments. so The positive and negative charges inside the glass atoms now also oscillate and generate their own electric and magnetic field. so the net electric and magnetic field at any instant will be the resultant of the fields produced by the original source as well as the fields produced by the charges inside atoms of glass.Hence as the directions of E- field and B- field change ,the corresponding poynting vector also changes. Hence the direction of light is changed.

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This doesn't really explain anything since when the two media have same index of refraction, there is no change of direction. The only important fact to explain here is the relation between index of refraction of the two media and the angle of refraction (i.e. the Snell's law). This is completely missing in this answer... –  Marek Aug 17 '11 at 8:38
actually, your answer explains the reason for propagation of light in matter...but not why it refracts!! –  Vineet Menon Aug 17 '11 at 8:45
Well Refraction is the change in the direction of propagation of light when it changes it medium of propagation. so I think my answer does explain. –  Primeczar Aug 18 '11 at 4:05
nOW when you speak of absence of refraction , I must say that the polarizing ability of an E-field is different for each and every materials wjose measure can be provided by its dielectric constant . –  Primeczar Aug 18 '11 at 4:07
so when two media are the same then the electric field generated by the osciallation of the charges inside each of the media will be along the same direction and so is the generated B-field. Hnece the poynting vector will mantain its direction. –  Primeczar Aug 18 '11 at 4:08

Your teacher's explanation, as you describe it, seems a little disengenuous. It is true that light goes from A to B in the shortest possible time, given different speeds in different media. From a human perspective, it almost seems like the light rays are calculating all their possible path options and picking the most optimal. The real question is, what is the physical mechanism that allows light to perform what appears to be the act of a rational being with infinite powers of calculation?

The answers to this question lie entirely within the domain of classical wave theory. There is no further insight to be gained by looking into the mysteries of quantum mechanics. Primeczar gives the bare outline of an explanation wherein the polarized charges within the glass are taken as the source of new fields. It's actually simpler to do the calculation if you simply accept that the propagation speed in glass is lower than air, and focus on the excess polarization that appears only on the surface of the glass, not within the body. It is then unnecessary to determine the amount of polarization, only to recognize that it must have some kind of constant phase relationship with the driving force of the incoming wave. The angle of refraction follows unambigously from this purely geometrical argument.

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Uh, what? Only QED can really explain why this happens. Otherwise you will have to stop somewhere along the road -- at the Snell's law or the Fermat's principle or the Maxwell's equations + matter interaction, etc. Perhaps one of those stops is fine for this answer but saying that "there is no further insight to be gained" is dead wrong and short-sighted... –  Marek Aug 17 '11 at 14:46
"Why?" and "really happend" are inherently subjective concepts, only "what" is fully objective in physics. But I personally do support a path integral / QED picture since it explains why least action principles are valid on a deeper level. At the same time by going quantum you open the door to other challenges to intuition... –  Slaviks Aug 17 '11 at 14:51
I would like to add that in classical electrodynamics any change in the boundary conditions, even at infinity changes the solutions, so in this sense the light "knows" where to go. Nevertheless, since this is a many body problem, the various laws are envelopes that provide a reason to the "why" that is more intuitive than a general path integral framework. –  anna v Aug 17 '11 at 15:38
Marek has me second-guessing my explanation somewhat, but only to the degree that I failed to clearly link the calculation method to the least-time outcome. I still think I could have done this entirely within a classical framework, so I don't see what additional insights would be gained from a QED treatment. As for the comparison of my method with Snell's Law or Fermat's Principle, I disagree. These are just calculational methods that give the right answer without any reason. My explanation actually provides a mechanism. –  Marty Green Aug 18 '11 at 0:13
Looking it up on Wikipedia, it appears to me that Fermat's Principle is indeed nothing more than the rule that light gets from A to B in the least amount of time. This doesn't explain why. If anything, Huygen's principle appears to be more in line with what I have called an explanation with a mechanism. Either way, I still do not know what further insights are gained from QED; and I am not aware of any corrections to classical trajectories are obtainable by a more complete QED treatment. If you are able to correct me on this I would be interested. –  Marty Green Aug 21 '11 at 0:38

The explanation is very simple! The reason light changes direction ("bends") when traveling through glass, is because light travels slower in glass than in air. If now, you also want to know why light travels slower in glass than air, it is because the density of glass is higher than air and the electromagnetic fields of the glass molecules interfere more, than the air molecules, with the propagation of light.

As you can see, no cognitive powers need be given, to light!

In general, light will "bend" any time it goes from one medium to another medium with higher or lower density. It is really the difference in densities that causes the bending of the light.

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It's not density but electromagnetic properties what matters, see my answer here: physics.stackexchange.com/a/68341/21817 –  jinawee Mar 2 '14 at 19:55

Light changes direction when passing through a prism because the density of air is different to the density of glass. Therefore the speed changes, when something (i.e. glass or a prism) is optically dense it is harder for light to travel through it, thus making it's speed decrease. When the waves meet the prism they slow down, so if they meet it at an angle part of the first part of the wave slows down first, leaving the remaining part to slow down later. This is what changes the direction and makes the light travel in a different way.

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It's not density but electromagnetic properties what matters, see my answer here: physics.stackexchange.com/a/68341/21817 –  jinawee Mar 2 '14 at 19:54

Electron & atomic beams also exhibit refraction.Deflection angle is due to the resistance to motion which depends on particle's size and medium's density. Photon behaves as particle in this effect.If it comes straight in,resistance pushes straight back and doesn't change direction.They call straight in or perpendicular to the surface "normal" in the Wikipedia article. If it comes in at an angle,the vector of resistance force is analyzed in two components: one parallel and one vertical to ("normal").The last component pushes the photon away from the "normal" direction.

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Have a look at the index of refraction, which is the ratio of the velocity of light in vacuum to the one in the medium. Light travels more slowly in a medium and thus "glances off" and changes direction, as in the drawing.

n = speed of light in a vacuum / speed of light in medium

For example, the refractive index of water is 1.33, meaning that in a vacuum, light travels 1.33 times as fast as it does in water.

I should add that refraction is observed in all types of waves,

Refraction is described by Snell's law, which states that the angle of incidence θ1 is related to the angle of refraction θ2 by


where v1 and v2 are the wave velocities in the respective media, and n1 and n2 the refractive indices. In general, the incident wave is partially refracted and partially reflected

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The question asks for the question "why", not "what"!! –  Vineet Menon Aug 17 '11 at 8:46
@Vineet Spelling it out: Because the indices of refraction are different in the two media, air and glass, or the wave velocities if you like, the angle in the second medium is different than the one in the first according to Snell's law. This is an answer to a why question, imo. –  anna v Aug 17 '11 at 13:06
@anna: I agree with Vineet that this is not an answer. The OP asks "why does refraction happen". You only stated how much the light refracts. But why does this happen? Where does the Snell's law come from? This is what is important (i.e. physics). –  Marek Aug 17 '11 at 13:59
@Marek I think the second link says that all waves refract due to the change in velocities, and gives some intuitive examples. The last paragraph of the first link goes into some detail in the microscopic view, without going into QED and path integrals, which is a level not comensurate to the question. –  anna v Aug 17 '11 at 15:28

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