Refractive index

[Craig Dilworth]

What is the most basic way of determining a medium's refractive index, and what does that method presuppose (e.g. a wave theory)?

[Cap'n Refsmmat]

Is this a homework problem, or are you just curious?

[swansont]

!

Moderator Note

I've moved this (and other posts) to HW help. 10 posts in 20 minutes, virtually all looking like HW questions. Nothing wrong with that, Craig, but don't expect people to do your HW for you. How about you discuss what you know and what the specific hangup in your knowledge is? May of the aspects of the questions look easily Google-able

[Mr Skeptic]

When you have that many questions, of a very general nature, you can be sure that the answers are all online. You could get your answers much more quickly and in as much detail as you care to read, by searching for them. Wikipedia will probably tell you all you need to know, otherwise Google search will find your answers.

 

It's just polite to do that before taking up real people's time asking for explanations to things you probably should have learned in class. In any case, that's probably better for whatever test you probably have coming up, both time-wise and for the detail. (The same goes even if this is not for a class).

[Craig Dilworth]

Is this a homework problem, or are you just curious?

 

This is not a homework problem and I'm not just curious. It got transferred from classical physics to homework by someone who obviously thought it was homework. I am investigating the foundations of modern physics, and this is one of the many questions I need an answer to. While I'm something of a neophyte in physics, I have a PhD in philosophy and have published a number of books in the philosophy of science.

 

Craig

[jackson33]

Craig, can I assume you are from Sweden?

[Craig Dilworth]

!

Moderator Note

I've moved this (and other posts) to HW help. 10 posts in 20 minutes, virtually all looking like HW questions. Nothing wrong with that, Craig, but don't expect people to do your HW for you. How about you discuss what you know and what the specific hangup in your knowledge is? Many of the aspects of the questions look easily Google-able

 

 

 

Swansontea,

 

I’m afraid I’ve given you the wrong impression. I just happened across Science Forums yesterday and saw it as an opportunity to answer questions I need answered for a work I’m doing on the foundations of physics. I’ve tried to answer these question by googling on them, but so far without success (though I have succeeded in getting many other questions answered through Google). But I could go more into the details behind each question, explaining why they've arisen.

 

My background is not that of a physicist, but a philosopher of science, though I have also done work in human ecology. Just now I am devoting my efforts to the foundations of physics, which means going back to the work of Römer, Newton, Huygens on up to Maxwell, Einstein, Bohr, Heisenberg, Bohm, Bell and all the rest.

 

If you know a ‘real’ physicist with an interest in these sorts of questions, you might mention me to him. Thanks!

 

 

I’ll attach my ongoing work on the topic so you can see what I’m up to. It's not a short-term thing. I plan to devote the rest of my life to it.

 

Best wishes,

 

 

Craig

 

 

When you have that many questions, of a very general nature, you can be sure that the answers are all online. You could get your answers much more quickly and in as much detail as you care to read, by searching for them. Wikipedia will probably tell you all you need to know, otherwise Google search will find your answers.

 

It's just polite to do that before taking up real people's time asking for explanations to things you probably should have learned in class. In any case, that's probably better for whatever test you probably have coming up, both time-wise and for the detail. (The same goes even if this is not for a class).

 

 

Dear Mr Skeptic,

 

This is a small number of questions compared to the number I have had. I thought I'd make them simple to start with, and then develop them more if I were to receive any replies. I assure you they constitute only the tip of the iceberg, the rest of the iceberg consisting of questions I have been able to answer through Google or Wiki. This is all in connection with a work I'm doing on the foundations of physics. I can send you my work in progress if you're interested.

 

My background is that of a philosopher of science, a subject in which I've published a number of books. (Google me!)

 

Thanks for taking the time to reply!

 

Best wishes,

 

Craig (Dilworth)

Dilworth - Foundations of Physics.doc

[imatfaal]

Not sure if Ole Romer isn't a little out of his league with that distinguished company - and surely a opening role for Galileo. Good luck on your work Craig..

 

[Craig Dilworth]

Craig, can I assume you are from Sweden?

 

 

Jackson33,

 

Yep. I'm a 61 year-old Canadian who has been living in Stockholm for the past 35 years (though just now I'm in Ottawa).

 

Craig

[jackson33]

Jackson33,

 

Yep. I'm a 61 year-old Canadian who has been living in Stockholm for the past 35 years (though just now I'm in Ottawa).

 

Craig [/Quote]

 

Yes, I know your work and that work and you have many entries listed on a simple google search. When I'm aware of a posters history however, it must be against the rules to divulge that history (have been warned). Anyway welcome to a seemingly sometimes unfriendly forum (homework LOL), but the best around for informal Science interaction IMO. I'm sure you will get some good answers in the future. Then I would be more interested in seeing you post under 'Philosophy'...

[Cap'n Refsmmat]

What is the most basic way of determining a medium's refractive index, and what does that method presuppose (e.g. a wave theory)?

 

To get around to answering your question:

 

Snell's law is the easiest method I am familiar with. Snell's law says:

 

[math]n_1 \sin \theta_1 = n_2 \sin \theta_2[/math]

 

n₁ and n₂ are the refractive indices of two media -- we have a light ray traveling from one medium into another. For example, suppose we have light going from air into a block of glass. The angle the light ray makes normal to the glass is the angle of incidence, [math]\theta_1[/math]. The angle the light makes normal to the surface when it's inside the block is [math]\theta_2[/math]. Given that the index of refraction of air is 1, we can solve for the refractive index of glass.

 

Snell's law can be derived several ways. You can use wave optics to derive it, or you can use the simple principle that light travels the path that takes the least time. Either will allow you to derive the law.

 

Another straightforward way would be to directly measure the speed of light in the medium, but that is more difficult.

[Craig Dilworth]

Yes, I know your work and that work and you have many entries listed on a simple google search. When I'm aware of a posters history however, it must be against the rules to divulge that history (have been warned). Anyway welcome to a seemingly sometimes unfriendly forum (homework LOL), but the best around for informal Science interaction IMO. I'm sure you will get some good answers in the future. Then I would be more interested in seeing you post under 'Philosophy'...

 

jackson33,

 

Thanks for your contact. Must have missed the bit about it being against the rules to divulge my history (if I've understood you right).

 

If your interested in my views on philosophy, keep a lookout for my new book Simplicity: A Metametaphysics. (Don't know who's going to publish it yet.)

 

Craig

 

To get around to answering your question:

 

Snell's law is the easiest method I am familiar with. Snell's law says:

 

[math]n_1 \sin \theta_1 = n_2 \sin \theta_2[/math]

 

n₁ and n₂ are the refractive indices of two media -- we have a light ray traveling from one medium into another. For example, suppose we have light going from air into a block of glass. The angle the light ray makes normal to the glass is the angle of incidence, [math]\theta_1[/math]. The angle the light makes normal to the surface when it's inside the block is [math]\theta_2[/math]. Given that the index of refraction of air is 1, we can solve for the refractive index of glass.

 

Snell's law can be derived several ways. You can use wave optics to derive it, or you can use the simple principle that light travels the path that takes the least time. Either will allow you to derive the law.

 

Another straightforward way would be to directly measure the speed of light in the medium, but that is more difficult.

 

 

Cap'n Refsmmat:

 

Many thanks for responding to my question.

 

As regards the basic way of determining a medium's refractive index, it would appear that it's essentially the relation between the angle of incidence and the angle of the ray inside the medium relative to the medium's surface (of course the angle of incidence is also relative to the medium's surface). If so, it seems its determination presupposes neither a wave nor a particle view. Have I got this right? (I'll look more closely at the conceptual background to Snell's law - thanks for mentioning it!)

 

But does determining the refractive index on the basis of the speed of light presuppose a wave theory? Hm, perhaps not. But if not, it would still have to give you the angle of incidence and the 'angle of refraction'; i.e. these angles are really what the refractive index is all about. Or?

 

Thanks again!

 

Craig

[swansont]

Must have missed the bit about it being against the rules to divulge my history (if I've understood you right).

 

!

Moderator Note

It's not inherently against the rules to reveal information about yourself. (It may be irrelevant, which might tread into that territory at some point; it depends on the circumstances). I think jackson was referring to one user revealing details of another poster; if e.g. one were to post using a pseudonym, it is not appropriate for someone else to reveal that user's real name. Similarly, the choice to reveal one's background or location, etc. is up to the user and not up to anyone else.

 

Also, I've moved the posts back to physics. Apologies for the delay (it's a bit of a pain since I don't see a way to do them in bulk)

[Cap'n Refsmmat]

Cap'n Refsmmat:

 

Many thanks for responding to my question.

 

As regards the basic way of determining a medium's refractive index, it would appear that it's essentially the relation between the angle of incidence and the angle of the ray inside the medium relative to the medium's surface (of course the angle of incidence is also relative to the medium's surface). If so, it seems its determination presupposes neither a wave nor a particle view. Have I got this right? (I'll look more closely at the conceptual background to Snell's law - thanks for mentioning it!)

Well, it relies on Fermat's principle, the idea that light travels the shortest possible path. This was proposed by Fermat before it was established that light is a wave, so clearly it's not dependent on a wave theory of light, but merely a treatment of light rays in general. However, one can mathematically derive Snell's law, and Fermat's principle, from a wave theory of light.

 

Snell's law was derived long before light was proved to be a wave, though, through various arguments.

 

But does determining the refractive index on the basis of the speed of light presuppose a wave theory? Hm, perhaps not. But if not, it would still have to give you the angle of incidence and the 'angle of refraction'; i.e. these angles are really what the refractive index is all about. Or?

 

They are. But only as a consequence of the fact that the refractive index is related to the speed of light inside that substance.

 

[math]n = \frac{\mbox{velocity of light in vacuum}}{\mbox{velocity of light in medium}}[/math]

 

Now, using a wave theory of light, one can determine that [math]n = \sqrt{\epsilon}[/math], where [math]\epsilon[/math] is the relative permittivity of the medium, which can be determined through other experimental means.

[Mr Skeptic]

Oh, OK.

 

What is the most basic way of determining a medium's refractive index, and what does that method presuppose (e.g. a wave theory)?

 

Well, if you know Snell's Law and the refractive index of one substance, you can use the equation and a measurement to measure the refractive index of a second substance. Note that for this method you need to be fairly confident about the shape of your object, so that you can properly measure the angles of incidence, though there might be a way to get around that with many measurements.

 

You can measure the speed of light in a substance and compare to the speed of light in a vacuum, and that would give you the index of refraction. For the second case you need more complicated equipment, but I think a laser rangefinder would work, though for accuracy you'd need to know some of the details of its operation. I'm pretty sure there's also specialized equipment to measure the index of refraction this way.

 

Early on refraction was considered evidence for the wave nature of light, but not really proof. You can model the same effect with solid objects; get a rectangular object and slide it at an angle toward the interface between two substances with different friction (higher friction would act like the higher index of refraction). If you push it toward the lower friction surface, when part of it sticks out to that side then the other side will have proportionately higher friction resulting in turning toward the high friction side, and likewise but opposite if you do it in the other direction.

 

To have the index of refraction, you need the speed of light to be a constant ratio in various substances (though I suppose for this purpose it wouldn't matter if the speed of light itself changed). This is satisfied by the speed of light having a constant speed in space and a constant speed in various substances depending on their index of refraction.

[Craig Dilworth]

Not sure if Ole Romer isn't a little out of his league with that distinguished company - and surely a opening role for Galileo. Good luck on your work Craig..

 

 

Thanks for your good luck wish Imatfaal!

 

Craig

 

!

Moderator Note

It's not inherently against the rules to reveal information about yourself. (It may be irrelevant, which might tread into that territory at some point; it depends on the circumstances). I think jackson was referring to one user revealing details of another poster; if e.g. one were to post using a pseudonym, it is not appropriate for someone else to reveal that user's real name. Similarly, the choice to reveal one's background or location, etc. is up to the user and not up to anyone else.

 

Also, I've moved the posts back to physics. Apologies for the delay (it's a bit of a pain since I don't see a way to do them in bulk)

 

!

Moderator Note

It's not inherently against the rules to reveal information about yourself. (It may be irrelevant, which might tread into that territory at some point; it depends on the circumstances). I think jackson was referring to one user revealing details of another poster; if e.g. one were to post using a pseudonym, it is not appropriate for someone else to reveal that user's real name. Similarly, the choice to reveal one's background or location, etc. is up to the user and not up to anyone else.

 

Also, I've moved the posts back to physics. Apologies for the delay (it's a bit of a pain since I don't see a way to do them in bulk)

 

Thanks Swansontea! Much appreciated.

 

Craig

 

Oh, OK.

 

 

 

Well, if you know Snell's Law and the refractive index of one substance, you can use the equation and a measurement to measure the refractive index of a second substance. Note that for this method you need to be fairly confident about the shape of your object, so that you can properly measure the angles of incidence, though there might be a way to get around that with many measurements.

 

You can measure the speed of light in a substance and compare to the speed of light in a vacuum, and that would give you the index of refraction. For the second case you need more complicated equipment, but I think a laser rangefinder would work, though for accuracy you'd need to know some of the details of its operation. I'm pretty sure there's also specialized equipment to measure the index of refraction this way.

 

Early on refraction was considered evidence for the wave nature of light, but not really proof. You can model the same effect with solid objects; get a rectangular object and slide it at an angle toward the interface between two substances with different friction (higher friction would act like the higher index of refraction). If you push it toward the lower friction surface, when part of it sticks out to that side then the other side will have proportionately higher friction resulting in turning toward the high friction side, and likewise but opposite if you do it in the other direction.

 

To have the index of refraction, you need the speed of light to be a constant ratio in various substances (though I suppose for this purpose it wouldn't matter if the speed of light itself changed). This is satisfied by the speed of light having a constant speed in space and a constant speed in various substances depending on their index of refraction.

 

So it seems I was mistaken in thinking that the index of refraction was a ratio relating angles to the common surface of the contingent media. It seems rather that they're ratios of the relative speeds in the two media. (Though I'm suspicious of this ...) But where I can imagine that the relevant angles can be determined without presupposing a particular optical theory, I wonder about determinations of the speed of light. The actual speed isn't measured directly, is it? Rather, it's inferred on the basis of theory. My guess would be Maxwell's (wave) theory. Or?

 

You say, "Well, if you know Snell's law and the refractive index of one substance ..." But, just to clarify, my considerations concern the situation prior to any knowledge of refractive index ... (And so, for example, I'm not interested in what may be accomplished using a modern laser rangefinder, nor in particularly accurate measurements ...)

 

I don't understand your example with a rectangular object. Could you develop it a little? I'm particularly interested in whether a particle theory can explain the phenomenon. Of course on the Newtonian view the speed of light was supposed to be faster the denser the medium, which has since his time been shown not to be the case, and has in fact been considered a serious flaw in the particle view. Do you know of any noteworthy attempts to develop the particle view in such a way that electrodynamic radiation slows down in denser media?

 

Many thanks for taking the time to deal with my question!

 

Craig

 

Well, it relies on Fermat's principle, the idea that light travels the shortest possible path. This was proposed by Fermat before it was established that light is a wave, so clearly it's not dependent on a wave theory of light, but merely a treatment of light rays in general. However, one can mathematically derive Snell's law, and Fermat's principle, from a wave theory of light.

 

Snell's law was derived long before light was proved to be a wave, though, through various arguments.

 

 

 

They are. But only as a consequence of the fact that the refractive index is related to the speed of light inside that substance.

 

[math]n = \frac{\mbox{velocity of light in vacuum}}{\mbox{velocity of light in medium}}[/math]

 

Now, using a wave theory of light, one can determine that [math]n = \sqrt{\epsilon}[/math], where [math]\epsilon[/math] is the relative permittivity of the medium, which can be determined through other experimental means.

[Cap'n Refsmmat]

So it seems I was mistaken in thinking that the index of refraction was a ratio relating angles to the common surface of the contingent media. It seems rather that they're ratios of the relative speeds in the two media. (Though I'm suspicious of this ...) But where I can imagine that the relevant angles can be determined without presupposing a particular optical theory, I wonder about determinations of the speed of light. The actual speed isn't measured directly, is it? Rather, it's inferred on the basis of theory. My guess would be Maxwell's (wave) theory. Or?

The index of refraction does relate angles of a light ray as it passes between two media, but its direct physical significance is a relative speed. As I said before, it is defined to be:

 

[math] n = \frac{\mbox{velocity of light in vacuum}}{\mbox{velocity of light in medium}} [/math]

 

...but it appears in Snell's law to relate angles as well.

 

You might look into the earliest determinations of the speed of light to see how it was done. It's not dependent on wave mechanics.

 

http://en.wikipedia...._speed_of_light

http://en.wikipedia....cault_apparatus

[Craig Dilworth]

But it seems to me something is 'backwards' here. Refractive index fundamentally concerns the angles of incidence and of refraction. That these can be determined on the basis of the speed of light is only possible given such things as that its speed is lower in denser media, and that we can rely on Maxwell's theory to (indirectly) tell us the speed of light in various media. A large part of my interest generally is in seeing how far one can go with a particle theory.

 

Thanks for taking up my question!

[Cap'n Refsmmat]

But it seems to me something is 'backwards' here. Refractive index fundamentally concerns the angles of incidence and of refraction. That these can be determined on the basis of the speed of light is only possible given such things as that its speed is lower in denser media, and that we can rely on Maxwell's theory to (indirectly) tell us the speed of light in various media. A large part of my interest generally is in seeing how far one can go with a particle theory.

 

Thanks for taking up my question!

 

The refractive index, despite its name, is defined in terms of the speed of light. I am not sure if you can explain the change of light's speed between mediums without a wave theory of light; the classical explanation is that each photon is absorbed and re-emitted by atoms in the medium, but I think that has a certain dependence on quantum mechanics. I'm not sure.

[John Cuthber]

The refractive index, despite its name, is defined in terms of the speed of light. I am not sure if you can explain the change of light's speed between mediums without a wave theory of light; the classical explanation is that each photon is absorbed and re-emitted by atoms in the medium, but I think that has a certain dependence on quantum mechanics. I'm not sure.

 

Snell did his work on refractive indexes before the speed of light was known. It would, therefore, have been quite difficult to have defined it that way.

The original definition came from measurements of how light travelled through media.

[Mr Skeptic]

So it seems I was mistaken in thinking that the index of refraction was a ratio relating angles to the common surface of the contingent media. It seems rather that they're ratios of the relative speeds in the two media. (Though I'm suspicious of this ...) But where I can imagine that the relevant angles can be determined without presupposing a particular optical theory,

 

Yup, the angles can be determined without the speed of light, but that is now the definition of the index of refraction.

 

I wonder about determinations of the speed of light. The actual speed isn't measured directly, is it? Rather, it's inferred on the basis of theory. My guess would be Maxwell's (wave) theory. Or?

 

Well, I measured it without using Maxwell's equations. I believe the first measurement involved bouncing light off rotating mirrors over a great distance. Basically, knowing the rate of rotation of the mirrors and the distance between them, allows you to calculate the speed of light (this in air, which is very close to in vacuum). The deal with maxwell's equations though, was a theoretical calculation of the speed of light and also with the really really old principle of relativity adds up to Einstein's special theory of relativity.

 

You say, "Well, if you know Snell's law and the refractive index of one substance ..." But, just to clarify, my considerations concern the situation prior to any knowledge of refractive index ... (And so, for example, I'm not interested in what may be accomplished using a modern laser rangefinder, nor in particularly accurate measurements ...)

 

Well yes, it's a ratio and you just choose one substance as the basis (in this case vacuum).

 

I don't understand your example with a rectangular object. Could you develop it a little? I'm particularly interested in whether a particle theory can explain the phenomenon. Of course on the Newtonian view the speed of light was supposed to be faster the denser the medium, which has since his time been shown not to be the case, and has in fact been considered a serious flaw in the particle view. Do you know of any noteworthy attempts to develop the particle view in such a way that electrodynamic radiation slows down in denser media?

 

Well, just go push a book around at an angle with the interface between two surfaces of different friction. Eg rug vs floor, polished vs unpolished floor, but the bigger the difference in friction the more noticeable the effect will be. See if the angle the book is traveling at changes. You might need to repeat that a few times since the materials will be rather crude.

[Craig Dilworth]

Snell did his work on refractive indexes before the speed of light was known. It would, therefore, have been quite difficult to have defined it that way.

The original definition came from measurements of how light travelled through media.

 

 

Thanks John!

 

Craig

 

Yup, the angles can be determined without the speed of light, but that is now the definition of the index of refraction.

 

[Great, thanks!]

 

Well, I measured it without using Maxwell's equations. I believe the first measurement involved bouncing light off rotating mirrors over a great distance. Basically, knowing the rate of rotation of the mirrors and the distance between them, allows you to calculate the speed of light (this in air, which is very close to in vacuum). The deal with maxwell's equations though, was a theoretical calculation of the speed of light and also with the really really old principle of relativity adds up to Einstein's special theory of relativity.

 

Well yes, it's a ratio and you just choose one substance as the basis (in this case vacuum).

 

Well, just go push a book around at an angle with the interface between two surfaces of different friction. Eg rug vs floor, polished vs unpolished floor, but the bigger the difference in friction the more noticeable the effect will be. See if the angle the book is traveling at changes. You might need to repeat that a few times since the materials will be rather crude.

 

[Gotcha! Thanks very much!]

[John Cuthber]

Newton may have been wrong, but he was jolly clever.

If he thought that a particle model would work, provided that they moved faster in the denser medium, then he must have had some sort of model to explain it. I don't know what it was, but I once met someone who might. I will see if I can find his webpage.

Found it

http://www.newtonproject.sussex.ac.uk/prism.php?id=45

 

Incidentally, the first measurements of the speed of light were astronomical. Fizeau's method (with wheels and distant mirrors) was a bit later.

I think it was Michelson and Morely who first measured the speed of light in water and got a direct proof that n was c/v but it might have been someone later.

Edited December 3, 2010 by John Cuthber

[Craig Dilworth]

Newton may have been wrong, but he was jolly clever.

If he thought that a particle model would work, provided that they moved faster in the denser medium, then he must have had some sort of model to explain it. I don't know what it was, but I once met someone who might. I will see if I can find his webpage.

Found it

http://www.newtonpro...prism.php?id=45

 

Incidentally, the first measurements of the speed of light were astronomical. Fizeau's method (with wheels and distant mirrors) was a bit later.

I think it was Michelson and Morely who first measured the speed of light in water and got a direct proof that n was c/v but it might have been someone later.

 

 

Thanks for the Newton link John. I've attached my work in progress, in case your interested in where I'm coming from. Craig

1 FP.doc