# Light speed and refractive index

• avicenna
In summary, according to the speaker, the speed of light in a non-vacuum medium is well-tested and measured using several methods. However, Snell's law is just a hypothesis, and has not been experimentally verified.f

#### avicenna

Refractive index of a medium is defined as : n = c / v; v is speed of light in medium.

I believe n is never measured directly as here is no way to directly verify c / v. So what I guess is that all refractive index values are experimentally measured using n = sin α₁ / sin α₂. But then there is circular logic here. So n = c / v is just a hypothesis which is not experimentally verified.

Refractive index of a medium is defined as : n = c / v; v is speed of light in medium.

I believe n is never measured directly as here is no way to directly verify c / v. So what I guess is that all refractive index values are experimentally measured using n = sin α₁ / sin α₂. But then there is circular logic here. So n = c / v is just a hypothesis which is not experimentally verified.
The calculations for the GPS signal uses the speed of light in air. And, I believe, even adjusts for varying air pressure.

In any case, the speed of light in non vacuum is well tested.

vanhees71 and Ibix
Show me how you measure the speed of light in glass.

There are several ways to measure the time of flight of light over a known distances, going back as far as the late 1840s, so I don't see why you would think you can't measure ##c/v##.

Please. Just give a a concrete example how you measure the speed of light in glass directly.

By the way, it also mean Snell's law is just a hypothesis; not experimentally veerified.

Please. Just give a a concrete example how you measure the speed of light in glass directly.
You get a light source and aim it through a block of glass of known thickness, to bounce off a mirror and come back. You time how long it takes a light pulse to return. Speed is distance over time. You need a decent clock and a more sophisticated design to control errors, but that's the gist of it.

A more sophisticated way is to use a Michelson interferometer. Put a block of glass in one arm and measure the optical path difference induced by the glass.

Last edited:
rsk and PeroK
By the way, it also mean Snell's law is just a hypothesis; not experimentally veerified.
Seriously? I measured angles of incidence and refraction in glass blocks and verified that the ratio of sines was constant, along with the rest of my class at school when I was about twelve years old. That's how routine experimental verification of Snell's law is.

Motore and etotheipi
By the way, it also mean Snell's law is just a hypothesis; not experimentally veerified.

Not to mention that not accepting Snell's law is equivalent to refuting rejecting the principle of least action

Last edited by a moderator:
Not to mention that not accepting Snell's law is equivalent to refuting the principle of least action
To be pedantic, it would be rejecting the principle of least action, rather than refuting. A refutation would be finding a real physical system that did not behave as predicted from the principle of least action, or showing a self-contradiction in a model that can only be resolved by abandoning the principle, or something of that sort.

(I'm aware that a lot of politicians use "I refute the allegation" to mean "they're lying, honest guv", but it's incorrect usage.)

etotheipi
To be pedantic, it would be rejecting the principle of least action, rather than refuting. A refutation would be finding a real physical system that did not behave as predicted from the principle of least action, or showing a self-contradiction in a model that can only be resolved by abandoning the principle.

(I'm aware that a lot of politicians use "I refute the allegation" to mean "they're lying, honest guv", but it's incorrect usage).

I'll take your word for it, I was never very good at Englishing

Show me how you measure the speed of light in glass.

Shoot a laser pulse at a beam splitter, with one leg leading to a mirror and the other leg leading to a block of glass and then a mirror. Now measure the difference in the timing of each pulse as it returns to the detector, account for the travel time through air/empty space, and divide the remaining difference by two. You now have the extra time it took for the light to travel through glass.

By the way, it also mean Snell's law is just a hypothesis; not experimentally veerified.

Nonsense. Snell's law is extraordinarily well supported by both experimental and theoretical evidence. Please make a better effort at understanding the topic before making such claims.

Ibix and PeroK
Seriously? I measured angles of incidence and refraction in glass blocks and verified that the ratio of sines was constant, along with the rest of my class at school when I was about twelve years old. That's how routine experimental verification of Snell's law is.
I am not refuting Snell's law on the sines of angles. My original doubt was about n = c/ v to explain Snell's law connection with refractive index.

I now remember Snell's law is proven based on certain least action principle... time to cover distance for light.

I believe n is never measured directly as here is no way to directly verify c / v.

You believe wrongly.
(Aside: You have a habit of coming here and not asking questions, but instead making incorrect statements and defending them. This is not a good idea.)

It is simple to do - put a light source on one side of a block of glass (or whatever) and a detector on the other and measure the time difference between emission and detection. With a 3 or 4 foot piece of glass it's about a nanosecond difference between glass and vacuum. This is easily doable in college undergraduate labs. You could almost do it with test equipment on sale at Fry's.

sophiecentaur, Ibix and PeroK
First of all you must be more precise which "wave speed" you want to measure. There are at least 3, which are important: The phase velocity, the group velocity, and the front velocity. The latter is to good approximation always the vacuum speed of light, while the others differ and can exceed the vacuum speed of light without violating relativistic causality. This issue has come up very early after Einstein's 1905 paper and was answered by Sommerfeld in 1907 in just a two-column article making an elegant argument using the theorem of residues. The longer answer is given by Sommerfeld and Brillouin in two famous articles in Ann. Phys. (1914). You find a shorter version in Sommerfeld's Lectures on Theoretical Physics vol. 4 and also in Jackson, Electrodynamics.

To measure the index of refraction (or rather the dieelectric tensor if you have an anisotropic material) of course you simply use the laws of reflection and refraction (aka Fresnel laws). Since there has never been any contradiction between theory and experiment in one of the most accurate branches of physics, optics, I don't understand, why you are in doubt about the issue.

sophiecentaur, Ibix and etotheipi
Please. Just give a a concrete example how you measure the speed of light in glass directly.
Is water acceptable instead of glass? Fizeau and Foucault did it in 1850, using two variations of the same principle.

https://en.wikipedia.org/wiki/Fizeau–Foucault_apparatus

When I was an undergraduate, we used a modern version of Foucault’s rotating-mirror apparatus to measure c in air. We could have done it in water if we had had a long enough tank (a few meters) with transparent sides.

Last edited:
sophiecentaur, vanhees71, Ibix and 1 other person
Please. Just give a a concrete example how you measure the speed of light in glass directly.
I am not refuting Snell's law on the sines of angles. My original doubt was about n = c/ v to explain Snell's law connection with refractive index.
It seems that you feel the need of a stop watch and a ruler before you can really believe this. A very long ruler is needed for this basic method.

But the phase of a wave is a perfectly valid way of measuring its transit time so (this idea has already been mooted above) split a light beam (monochromatic is best) into two equal length paths. An interference pattern (fringes) will form where the beams coalesce and note just one maximum. If you slowly slide a wedge of glass into one of the beams, this maximum will move to the side. Moving the wedge further and further into the path will cause the the fringes to move steadily one way. Count the number of maxima going past a datum and that will tell you the number of wavelengths by which the light path through the glass has shortened. That will tell you the amount by which the speed has affected the path length and that gives the transit time. So you have a time and a distance - which gives you the speed through the glass (compared with the air path). Any other combination of path materials are possible for the same basic experiment.
You can breathe a sigh of relief that Snell is justified and confirmed.

Ibix and vanhees71
Just for interest: I once tried to demonstrate that the sound of a bell inside a bell jar, which we evacuate with a pump, cannot be heard, whilst at the same time microwaves travel through the jar undisturbed. Unfortunately for me (as often happens), the microwaves decreased slightly with the vacuum. I conjectured that this is because the vacuum has a lower permittivity than air, and so the microwaves speed slightly up in the jar and we have a convex diverging lens.

The difference in permittivity is extremely small. I'd put the effect down to some distortion, somewhere in the layout of the signal path (change in impedance of the feed or even supply volts). Your 'optics' idea actually makes little sense, imo. When does a convex lens 'diverge'?

The difference in permittivity is extremely small. I'd put the effect down to some distortion, somewhere in the layout of the signal path (change in impedance of the feed or even supply volts). Your 'optics' idea actually makes little sense, imo. When does a convex lens 'diverge'?
With a "normal" lens the light slows down on entering the glass and is bent towards the normal. But if the lens is made of something which allows light to speed up, then the light is bent the opposite way. In other words, away from the normal. So a convex lens becomes a diverging lens. In my demonstration I had a giant galvo indicator to show the received microwave power, and the class quickly spotted the slight reduction.

then the light is bent the opposite way.
I am a duffer as I didn't spot that. But actually the lens would would become a plano-concave lens section if the source were inside.
But how much did the level change by? The permittivity change is about 0.06%. Do you reckon you saw that? Microwave lenses use plastic foam to get any significant refractive effect.

I taught a freshman lab where we had lenses of air that the students put in water tanks. Concave lenses were (probably still are) converging and convex were diverging.

tech99, sophiecentaur and vanhees71
I am a duffer as I didn't spot that. But actually the lens would would become a plano-concave lens section if the source were inside.
But how much did the level change by? The permittivity change is about 0.06%. Do you reckon you saw that? Microwave lenses use plastic foam to get any significant refractive effect.
Regarding refractive materials for microwaves, I made a big prism, about 200mm side, from paraffin wax. This worked similarly to an optical one, including the demonstration of total internal reflection. In about 1895, Jagadish Chandra Bose used a thick copy of the Rail Timetable to demonstrate double refraction effects using 30 GHz. In the case of the bell jar, maybe the slight change in permittivity causes noticeable ray bending; the optical lever comes to mind.

sophiecentaur
Different air temperatures in atmospheric layers affect propagation of microwaves but that involves long path lengths ( Kilometer distances and very shallow angles) . Paraffin and paper have significant relative permittivity to allow lens experiments and foam is a good practical medium).
Air / vacuum , I doubt. I’m skeptical about any explanation of the school bell jar experiment that involves 0.06% changes in refractive index. There are many other reasons for a school demo to give strange results. Before accepting that explanation it would involve some serious ball park calculations, using Snell’s law.

to measure the speed of light in material media,
here are some possibly useful set-ups:

(in a fiber optic)

(in air, but you can insert a glass block)

(PASCO)

(using interference fringes)

(You can also search for measurements involving microwave ovens and
chocolate or marshmallows (but that's not easily adapted to use glass as a medium).)

Ibix
There are at least 3, which are important: The phase velocity, the group velocity, and the front velocity. The latter is to good approximation always the vacuum speed of light, while the others differ and can exceed the vacuum speed of light without violating relativistic causality.
How is phase velocity related to deflection angle?

You get all this by solving the Maxwell equations for an electromagnetic wave going through two different media. Together with the boundary conditions what you get are the laws of reflection and refraction in terms of the Fresnel coefficients:

https://en.wikipedia.org/wiki/Fresnel_equations

binis