# Why does light travel slower in water?

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• student34
In summary, according to this explanation, the light changes direction because the individual water molecules absorb and reabsorb it.
student34
I always thought it was from individual water molecules absorbing and reabsorbing light, but this explanation in a video from Fermilab is very strange to me .

What is this "new wave" he speaks of; wouldn't it be light too? If so, then this light is now slower than the speed of light, which makes no sense.

I think the idea of the video is correct. One can show that Maxwell's equations admit plane wave solutions with phase velocity ##1/\sqrt{\epsilon \mu}##. In most cases ##\mu \sim \mu_0##, so it's only required to consider the dependencies of ##\epsilon##. You could say that an electron paired to a positive core obeys a damped, driven oscillatory equation of motion of the form\begin{align*}
\ddot{x} + 2\gamma \dot{x} + \omega_0^2 x = eE(t)/m
\end{align*}with ##E(t)## varying harmonically with time, and this equation is then easily solved for ##x(t)##. If there are ##n## such oscillators per unit volume, then the polarisation of the medium is related to the electric field by ##P = ne\bar{x} = \chi \epsilon_0 E##, which enables you to determine ##\epsilon = \epsilon_0(1+\chi)##; this depends on the freqency ##\omega## of the electric field.

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Spinnor, sysprog and PeroK
ergospherical said:
I think the idea of the video is correct, but not fleshed out. One can show that Maxwell's equations admit plane wave solutions with phase velocity ##1/\sqrt{\epsilon \mu}##. In most cases ##\mu \sim \mu_0##, so it's only required to consider the dependencies ##\epsilon##.

Following the approach of the video, you could say that an electron paired to a positive core obeys a damped, driven oscillatory equation of motion of the form\begin{align*}
\ddot{x} + 2\gamma \dot{x} + \omega_0^2 x = qE(t)
\end{align*}with, say, ##E(t)## varying harmonically with time, and this equation is then easily solved for ##x(t)##. If there are ##n## such oscillators per unit volume, then the polarisation of the medium is related to the electric field by ##P = ne\bar{x} = \chi \epsilon_0 E##, which enables you to determine ##\epsilon = \epsilon_0(1+\chi)##; this depends on the freqency ##\omega## of the electric field.
But what is this "new wave"? Is it light, or what?

student34 said:
But what is this "new wave"? Is it light, or what?
both waves, and the resultant composite wave, are electromagnetic waves which, at a certain range of frequencies, we call light. The words are a human construct and don't matter to nature at all.

What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.

phinds said:
both waves, and the resultant composite wave, are electromagnetic waves which, at a certain range of frequencies, we call light. The words are a human construct and don't matter to nature at all.

What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.
But aren't all EM waves light, which are suppose to travel at the speed of light?

student34 said:
But aren't all EM waves light, which are suppose to travel at the speed of light?
Yes, but you aren't paying attention to the COMPOSITEness of the resultant wave as explained by the math in post #2. The waveform of the incident light is combined with the created electromagnetic wave from the electrons.

Also, NO, not ALL EM waves are "light". As I said in the first place "light" is a term we usually only apply to that range of EM frequencies that stimulate our optical nerves.

student34 said:
But aren't all EM waves light, which are suppose to travel at the speed of light?
Light in vacuum travels at the speed of light in vacuum, denoted by ##c##. Light in a medium travels at ##\dfrac c n##, where ##n## is the refractive index of the medium. Note that ##n = 1## for vaccum.

A postulate of special relativity is that light travels at ##c## in vacuum, as measured in any IRF. There is no postulate that light travels at ##c## in water.

student34 said:
If so, then this light is now slower than the speed of light, which makes no sense.
c only applies in a vacuum. Anything present will slow it down.
student34 said:
individual water molecules absorbing and reabsorbing light,
A simple approach: A light wave passing a molecule will only be 'absorbed' under certain conditions. What we all learned about the Hydrogen Atom absorbing or emitting some specific wavelengths doesn't apply for most wavelengths and most atoms, molecules, liquids or solids. Particularly, when light passes through a solid or liquid (very dense), it interacts with all the material along its path and slows down noticeably but Energy loss is not significant - unlike actual absorption processes. Coming out of the other side, c is re-established. There is no mechanical 'deceleration' and 'acceleration' as with particles that have mass so the change of speed need not worry you.

I think these Sixty Symbols videos are good:

davenn
student34 said:
this light is now slower than the speed of light, which makes no sense.
One important thing to realize about ##c## is that it is the speed of light in vacuum, although those last two words are often omitted for brevity. I would say Lincoln probably would have been wise to have included them in this particular video, but he has more YouTube followers than I do. Either way, light in a medium not traveling at the speed of light in a vacuum is not an oxymoron.
student34 said:
But what is this "new wave"? Is it light, or what?
I would describe that "new wave" as "a light wave in a medium". Take a look at the diagrams around 8:30 (and the earlier ones around 7:03) in Lincoln's video, where he's showing two waves adding to make a third. I would say that those diagrams are actually the reverse of the argument he's making. I would say that his argument is that if you take the real electromagnetic field present in the medium (analogous to the third wave) and subtract something that looks like a light wave in vacuum (analogous to the first wave), the remainder (analogous to the second wave) turns out to look like the wave that would be emitted by atomic electrons that just happened to be oscillating as if they'd been driven by the light.

So Lincoln's "new wave" is the physical reality - a light wave in a medium. The other two waves are notional - we can't physically split an EM field into two separate EM fields, only split the mathematical description into two separate terms. But the split up terms do provide some physical insight.

Spinnor and sophiecentaur
Thanks everyone

davenn and berkeman
All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?

Psnarf said:
All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?
Maxwell's equations represent the classical theory of Electromagnetism. No photons, no probabilities.

In QED, the quantum mechanical theory of light, there would be an alternative explanation for the speed of light in glass. And, QFT (quantum field theory) would give the most fundamental explanation, involving the interaction of several quantum fields. This would be much more complicated than using Maxwell's equations, which are the coarse-grained consequences of QFT in this scenario.

Ibix
Photons aren't point particles and no position operator is defined for them, so they don't have an exact location. Learning the maths has been on my to-do list for a while, but my understanding is that even when thinking in quantum terms, "wave" is a nearer description of traveling light than "stream of particles".

phinds said:
What gets me is that he says absolutely nothing about why the light changes direction when it enters the glass.
I seem to recall that the direction is determined by the boundry conditions at the interface necessary to reconcile the continuity of the EM field at the interface. It is in the math.

pinball1970 and PeroK
Psnarf said:
Maxwell's equations predict the probability of finding a photon.
I think 'they' would say that's OK but, on the way, a photon can't be said to exist anywhere. A photon is what interacts (in quanta) with an object with mass. That's a particularly hard idea in the case of a transparent substance which passes the energy through it without changing its frequency but absorbing some of the energy. Try to make sense of that in terms of light photons with energy hf passing through glass and just losing 1% of the energy of the beam.

gleem said:
I seem to recall that the direction is determined by the boundry conditions at the interface necessary to reconcile the continuity of the EM field at the interface. It is in the math.
I tried to read about this (change of direction) before asking. I did not get far on the why. Plenty on how to work it out given the angles.
Without the maths is the why out of reach? I don't understand the time side of it either if I am honest. Compositeness of the waves. Is there a heuristic explanation?

pinball1970 said:
I tried to read about this (change of direction) before asking. I did not get far on the why. Plenty on how to work it out given the angles.
Without the maths is the why out of reach? I don't understand the time side of it either if I am honest. Compositeness of the waves. Is there a heuristic explanation?
There's a heuristic explanation that one side of the wavefront hits the glass first and slows down and sort of pulls the rest of the wavefront round. It's a model that might work better for a physical object, perhaps.

pinball1970
The frequency is constant across the interface and the velocity decreases, so the wavelength must decrease. There needs to be an angle between the propagation directions in order that waves of different wavelengths "match" at the interface.

pinball1970
pinball1970 said:
Plenty on how to work it out given the angles.
Without the maths is the why out of reach?
"without the maths" we can't even work out the price of two litres of petrol at £1.40 a litre. There can be no surprise that, without a bit of Trigonometry, you can't derive Snell's Laws of refraction. Are you suggesting that we should require statements made in the 17th Century to explain Nuclear Physics?

I think I can simplify this for you... c = the speed of light in a vacuum, if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons, there is a propagation delay while this transformation from a photon to a more energetic electron and back to a photon occurs. While it may appear that light travels slower, it would be correct to say light propogates slower through water than say through air. photons always travel at c.

weirdoguy, Vanadium 50, DaveE and 1 other person
Growler said:
if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons,
This is incorrect, as the video in the OP explains.

li
Psnarf said:
All this time I thought light was a stream of photons. Maxwell's equations predict the probability of finding a photon. So, we're back to waves now?
light as demonstrated in the dual slit experiment has both a particle and a wave nature... in fact, everything in the universe has a wave function.

Ibix said:
This is incorrect, as the video in the OP explains.
Encounter does not equate to collisions, in quantum physics there are no collisions, just interactions. these interactions take time.

Growler said:
I think I can simplify this for you... c = the speed of light in a vacuum, if light travels through any substance it encounters atoms and particles, each absorbs and re-emits the photons, there is a propagation delay while this transformation from a photon to a more energetic electron and back to a photon occurs. While it may appear that light travels slower, it would be correct to say light propogates slower through water than say through air. photons always travel at c.
OK, then you'll need to explain how a "re-emitted" photon travels in exactly the same direction as the others and is emitted with exactly the same delay as the others. In other words, why doesn't the light disperse in space and time? Also, why is glass equally transparent to many wavelengths, since atomic absorption tends to have specific energy levels?

Watch those videos.

Growler said:
Encounter does not equate to collisions, in quantum physics there are no collisions, just interactions. these interactions take time.
Given that precisely that explanation is debunked in Dr Lincoln's video leaves us less than impressed by your grasp of quantum electrodynamics, I'm sorry to say.

DaveE said:
OK, then you'll need to explain how a "re-emitted" photon travels in exactly the same direction as the others and is emitted with exactly the same delay as the others. In other words, why doesn't the light disperse in space and time? Also, why is glass equally transparent to many wavelengths, since atomic absorption tends to have specific energy levels?

Watch those videos.
1. it does not travel in "exactly" the same direction, reference diffraction, dispersion, scattering etc. how would you measure the progress of individual photons to determine the delay of each?
2. the absorption of the energy of the photon and the re-emission is just one example of propagating interaction... gravitation plays a role, wave interference etc. it still comes down to propagation delay.

You might consider these interactions "negligible" however consider that time itself is dilated to
a very small extent by the higher gravitational distortion in a denser ambient... even this will manifest an apparent departure from c.

IMHO these videos in one fell swoop both over complicate and over simplify.

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weirdoguy and fresh_42
DaveE said:
since atomic absorption tends to have specific energy levels?
Only for isolated atoms and molecules (gases). In dense materials, the Pauli Exclusion principle applies and the lines become broad bands. The interaction with water is with very high numbers of molecules - all over the wave front. Refraction is also a diffraction effect (as ever) as the wave crosses the boundary.

Growler said:
how would you measure the progress of individual photons to determine the delay of each?
That is actually a flawed concept. Photons do not "progress" as their position and extent is unknown.

sophiecentaur said:
That is actually a flawed concept. Photons do not "progress" as their position and extent is unknown.
My point exactly

sbrothy and sophiecentaur

## 1. Why does light travel slower in water?

Light travels slower in water because it is a denser medium compared to air. This means that the molecules in water are more tightly packed, causing the light to interact more frequently with the molecules and thus slowing down.

## 2. Does light always travel slower in water?

Yes, light always travels slower in water compared to air. However, the speed at which light travels in water can vary depending on factors such as temperature and salinity.

## 3. How much slower does light travel in water compared to air?

The speed of light in water is approximately 75% of the speed of light in a vacuum, which is the speed at which light travels in air. This means that light travels about 25% slower in water compared to air.

## 4. Can light travel at different speeds in different types of water?

Yes, the speed of light in water can vary depending on the type of water. For example, light travels faster in freshwater compared to saltwater due to the difference in density between the two types of water.

## 5. How does the speed of light in water affect the appearance of objects underwater?

The slower speed of light in water causes a phenomenon known as refraction, which is the bending of light as it passes through a different medium. This can affect the appearance of objects underwater, making them appear closer or distorted compared to how they would appear in air.

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