Does Snell's Law accurately explain light refraction in water?

[Buckethead]

I was reading a book called Catching the Light; a book on the history and other interesting things about light. There is a discussion in the book about refraction such as one might see when looking at a stone at the bottom of a pond when viewed at an angle. I've always just thought of the bending of the light beam at the surface as due to the change in medium and never gave it much thought past that. However, in this book refraction is described as the path that light can and will take to minimize the amount of time it takes for the light to get from the stone to the eye of the observer. It turns out a straight line path is not the shorted time as the light has to propagate through more water (where it travels at less than c) than it would if it followed a shorter path to the surface, and then a longer path to the eye. Too far and the light time increases again due to the longer distance through the air which is why the light doesn't just go straight up then over to the eye.

This description of light seems sensible and considering the strange nature of quantum physics, doesn't seem to be unreasonable. So my question is: Is this really what happens?

 

[kuruman]

This description of light seems sensible and considering the strange nature of quantum physics, doesn't seem to be unreasonable. So my question is: Is this really what happens?

Yes, light actually travels slower in a transparent medium that in vacuum. When it goes in from A in medium 1 to B in medium 2, say air and water, it travels in a straight line in each medium but not in a straight line from A to B. The path it follows minimizes the overall time of travel from A to B.

 

[sophiecentaur]

Snell's Law is actually the result of the time thing. Fermat's Principle of least time makes the lengths of the rays a minimum when sin i / sin r is a constant for two media.

Is this really what happens?

Achtung! That question is verboten in Science. There are often several alternative descriptions for a Physical Phenomenon, some may be more accurate than others but we only select the most accurate and general description and not because it is really what happens. Any of the current Models in Science could be disproved or extended tomorrow and a real Scientist would be chuffed about it if it happened. (But Scientists are also human beings so they don't give up without a struggle.)

 

[Buckethead]

The path it follows minimizes the overall time of travel from A to B.

Wow! I find this astonishing.

Achtung! That question is verboten in Science. There are often several alternative descriptions for a Physical Phenomenon, some may be more accurate than others but we only select the most accurate and general description and not because it is really what happens. Any of the current Models in Science could be disproved or extended tomorrow and a real Scientist would be chuffed about it if it happened. (But Scientists are also human beings so they don't give up without a struggle.)

I stand corrected. Yes, of course. I should know better by this time as all science can really do is describe what nature is doing, but never explain why it is doing it.
However, taking this right up to the no-no point, has there been any speculaton as to why and how a light beam can "know" the shortest (timewise) path? You have to admit this really makes one wonder.

 

[kuruman]

However, taking this right up to the no-no point, has there been any speculaton as to why and how a light beam can "know" the shortest (timewise) path? You have to admit this really makes one wonder.

Read this little book described here. It is meant for non-experts and it is wonderfully written by a master teacher and top physicist.
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

 

[sophiecentaur]

how a light beam can "know" the shortest (timewise) path?

I think that's an easy one. A light 'beam' is just the result of the shape of a wave front. An'ideal' light ray is a figment because, to be in a specific direction, the width of the wave front would need to be infinite. If you look at the Huygen's principle for plotting the progress of a wave, the wave doesn't have to 'know' the future of its path, it just moves, a step at a time and follows the rules about its wavelength in each bit of each medium. The ray's path is just the result of all the wavelets adding up on each wave front.

You have to admit this really makes one wonder.

Yes. I wondered and then I thought about what I have learned about wave propagation.

 

[ZapperZ]

Wow! I find this astonishing.

I stand corrected. Yes, of course. I should know better by this time as all science can really do is describe what nature is doing, but never explain why it is doing it.
However, taking this right up to the no-no point, has there been any speculaton as to why and how a light beam can "know" the shortest (timewise) path? You have to admit this really makes one wonder.

Actually, this is more general than just for light.

There is another side to the way we describe our world in terms of forces. It is in terms of energy. In this type of description, "forces" really doesn't play a major rule, unlike how it is in Newtonian description.

One aspect of this description is something called the Principle of Least Action. Fermat's Least Time principle as applied to light is one such application of this Least Action principle. It is a section of mechanics that a lot of people probably are not aware of if they never go beyond intro college general physics courses. In advanced mechanics, this leads to the Lagrangian/Hamiltonian formulation of mechanics. It is not a coincidence that we have a "Hamiltonian" in quantum mechanics as well.

What this means is that this is a general way to describe our universe, similar to how we used forces. So light has no choice in being formulated this way, because that is how our universe is.

Zz.

 

[Dale]

Adding on to what Zz said, the amazing thing to me is that this least action principle appears to be something where the system somehow knows the future so that it can choose the path which minimizes the action over the whole path. But in fact the global path minimizing formulation is completely equivalent to Newton’s force description where the whole path is clearly not known.

So my take away from that is that just because there is a strange “know the future” formulation, doesn’t mean that there isn’t also a “here and now only” formulation. And the two are completely equivalent!

 

[sophiecentaur]

So my take away from that is that just because there is a strange “know the future” formulation, doesn’t mean that there isn’t also a “here and now only” formulation. And the two are completely equivalent!

The requirement to 'know the future' is often assumed but many situations are only described adequately when a steady state has been reached. Light passing through a pair of semi-reflecting mirrors (etalon filter) requires many internal reflections to take place before the frequency response to be established. Even with a simple resistor circuit, we frequently get the question "how does it know what current to allow through?".
The Maths of these situations ignores this problem and just applies the steady state conditions to get (predict) an answer. It's not surprising that people are disturbed and unsatisfied by the School Level explanations.

 

[Bandersnatch]

Read this little book described here. It is meant for non-experts and it is wonderfully written by a master teacher and top physicist.
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

There's also the wonderful public outreach lectures Feynman gave on the same subject:
http://www.vega.org.uk/video/subseries/8

 

[ZapperZ]

Addendum:

Edwin Taylor has been an advocate of teaching the Principle of Least Action at all levels. His webpage has a wealth of publications on this topic that one might want to look at if one is not familiar with this concept.

Zz.

 

[Al_]

Important to note, I think, that light does not choose that particular path from the start. It emanates in all directions, and you simply see the light that ends up at your eye.
The light you see, because it headed off in the direction that gets it to your eye, is also the light that gets to your eye first. But it's also the only light that gets to your eye.
BUT, here's the odd thing. What if, directly in line between the stone and your eye, you place a glass in the surface water so that it has a flat surface perpendicular to the line of sight? Now, that light gets to your eye too. You see two stones. But the one you see through the glass has light that gets there slower.

 

[Buckethead]

Read this little book described here. It is meant for non-experts and it is wonderfully written by a master teacher and top physicist.
https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

Thanks for the tip. I bought the book and am looking forward to reading it. Nothing like a little Feynman and his humor to put a smile on one's face.

 

[Buckethead]

One aspect of this description is something called the Principle of Least Action. Fermat's Least Time principle as applied to light is one such application of this Least Action principle

This principle I see was derived from the Huygen's principle. Fascinating how one principle just leads to another which leads to another. I'll need to try and study both Huygen's principle and Fermat's principle to get a better handle on this.

 

[Buckethead]

Adding on to what Zz said, the amazing thing to me is that this least action principle appears to be something where the system somehow knows the future so that it can choose the path which minimizes the action over the whole path.

Exactly!

But in fact the global path minimizing formulation is completely equivalent to Newton’s force description where the whole path is clearly not known.

I'm not sure what you mean by this.

So my take away from that is that just because there is a strange “know the future” formulation, doesn’t mean that there isn’t also a “here and now only” formulation. And the two are completely equivalent!

Yes, and you know what I like about that? For those cases where the two are not only equivalent, but also turn out to be accurate descriptions but based simply on different premises, this can lead to a new hypothesis as to why two different ways to describe one event are equivalent. In other words, why would there be the coincidence that two hypothesis can accurately describe something using two seemingly unrelated premises. I'm not sure if what I'm saying actually pans out in practice, but it seems to me it should. Surely there must be examples of this in history.

 

[Buckethead]

The requirement to 'know the future' is often assumed but many situations are only described adequately when a steady state has been reached. Light passing through a pair of semi-reflecting mirrors (etalon filter) requires many internal reflections to take place before the frequency response to be established. Even with a simple resistor circuit, we frequently get the question "how does it know what current to allow through?".

More brain candy. Just like refraction, never really gave it much thought over, "well, it's probably like a sand clock and that's good enough for me". I'm going to start thinking about that one now ;)

 

[Buckethead]

Addendum:

Edwin Taylor has been an advocate of teaching the Principle of Least Action at all levels. His webpage has a wealth of publications on this topic that one might want to look at if one is not familiar with this concept.

Zz.

Great! Thanks.

 

[scottdave]

Here is an interesting application of the math of Snell's Law in this Mind Your Decisions video.