# Light Regaining energy?

## Main Question or Discussion Point

Hello. I was wondering, if light from a star (for arguments sake take our sun) emits light, and the light passes through a planets atmosphere (again for arguments sake, take our own planet Earth), it slows down as it moves into the denser area of our atmosphere. Say then it left the atmosphere again, it has lost energy while slowing down, and that energy has been converted into heat energy. Once it leaves the atmosphere, does the light "re-accelerate" back to the speed of light in a vacuum or does it remain the same speed as it was in the denser area of the atmosphere? If it does, where does the additional energy for the acceleration come from?

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I dont think the light looses energy when it slows down in a medium. The energy of light is a function of its frequency, its not like the usual one half m v squared.

If you look closer at light you see that it does move at the speed of light in between atoms, the fact that it appears to move slower is from the interaction with the atoms (it picks up a phase shift I believe, which effectively slows it down)

So (excuse the naive question) where does the heat energy come from in say a sheet of glass, when light shines through it?

russ_watters
Mentor
The glass absorbs some of the light trying to pass through it.

I hope this isn't hijacking the thread, but it makes me wonder if the limit C is actually the result of a lower limit to the emptiness of space. In other words, I wonder if the absorption and re-emission through very sparse particles is actually what is responsible for light slowing down to C - and if in fact light actually travels instantaneously between particles if there's nothing in between them, even if they would be very far apart.

diazona
Homework Helper
I hope this isn't hijacking the thread, but it makes me wonder if the limit C is actually the result of a lower limit to the emptiness of space. In other words, I wonder if the absorption and re-emission through very sparse particles is actually what is responsible for light slowing down to C - and if in fact light actually travels instantaneously between particles if there's nothing in between them, even if they would be very far apart.
Not sure if this is hijacking... but regarding light: no, that is not the case. The speed c is the speed of light in empty space, i.e. the speed it takes between particles when there is nothing in the way. Absorption and re-emission do occur when there are particles in the way, and they slow down the overall speed of light to less than c. How much less depends on the material.

If you've ever heard of the index of refraction, it's defined for any given material as the ratio of (speed of light in empty space)/(speed of light in material). For example, water has an index of refraction of about 1.33, so light travels through water with a net speed of about c/1.33.

Not sure if this is hijacking... but regarding light: no, that is not the case. The speed c is the speed of light in empty space, i.e. the speed it takes between particles when there is nothing in the way. Absorption and re-emission do occur when there are particles in the way, and they slow down the overall speed of light to less than c. How much less depends on the material.

If you've ever heard of the index of refraction, it's defined for any given material as the ratio of (speed of light in empty space)/(speed of light in material). For example, water has an index of refraction of about 1.33, so light travels through water with a net speed of about c/1.33.
How is it measured in a complete vacuum?

diazona
Homework Helper
How is it measured in a complete vacuum?
Laser ranging experiments in space, for example. Now, it's true that even space is not a complete vacuum, but if that bothers you, does it really make sense that something like a couple of atoms per cubic meter would cause a major change in the speed of light?

Laser ranging experiments in space, for example. Now, it's true that even space is not a complete vacuum, but if that bothers you, does it really make sense that something like a couple of atoms per cubic meter would cause a major change in the speed of light?
How many molecules would have to absorb and re-emit light over 300,000km? How far can light travel through atmospheric air in one second? Shouldn't the speed of light control for the million or so particles that light has to travel through to make it through 300,000km of "empty" space, for the sake of accurate comparison?

diazona
Homework Helper
What, are you saying we should define the constant c to be the speed that light actually travels through space, rather than the speed it takes through a theoretical pure vacuum? That would be silly, because for one thing the constant c has other meanings besides just being the speed of light through a vacuum. In fact, you could argue that it makes more sense to define it as the unique invariant speed required by the theory of relativity, and that definition is not affected by the presence of matter.

Also, what if you were in a patch of space with a lower density of matter? Intergalactic space, for example? Would you have to raise the speed of light to compensate for the lower density? The appeal of the fundamental constant c is that it's universal, it takes the same value everywhere, regardless of local conditions.

Also, even in the space surrounding the Earth (once you get far enough up, a few hundred km), the density is so low that if you shine a laser in some direction, most of the photons in that laser beam will travel 300,000 km and more without ever hitting a molecule.

Also, what's so special about 300,000 km anyway? You could shine a laser half a mile and measure the time it takes.

And - I really should have thought of this before - getting light to travel a given distance and timing it is not even the best way to measure its speed. You can actually do it better with an interferometer, which is a device that splits a light beam into two, sends them down different paths, and recombines them at a receiving screen. What you wind up seeing is a set of "fringes" which shift position as the length difference between the two paths changes, and the exact rate at which they shift position depends on the speed of light. So you can measure the shift and use it to calculate the speed.

What, are you saying we should define the constant c to be the speed that light actually travels through space, rather than the speed it takes through a theoretical pure vacuum? That would be silly, because for one thing the constant c has other meanings besides just being the speed of light through a vacuum. In fact, you could argue that it makes more sense to define it as the unique invariant speed required by the theory of relativity, and that definition is not affected by the presence of matter.
The reason why this whole issue came up was because I was wondering if absorption and re-emission through sparse particles in outer space would account for the speed of light being what it is "in a vacuum," i.e. 300,000km/s. I wondered if those particles were not there, would it actually travel faster (like in intergalactic space for example, as you mentioned).

Also, what if you were in a patch of space with a lower density of matter? Intergalactic space, for example? Would you have to raise the speed of light to compensate for the lower density? The appeal of the fundamental constant c is that it's universal, it takes the same value everywhere, regardless of local conditions.
Yes, but I would like to know what its speed would be in an absolute vacuum, or rather I should say in between particles, by controlling for the time it takes for particles to absorb and re-emit it, even in deep space.

Also, even in the space surrounding the Earth (once you get far enough up, a few hundred km), the density is so low that if you shine a laser in some direction, most of the photons in that laser beam will travel 300,000 km and more without ever hitting a molecule.
How would that be possible if every square meter contain several molecules? What are the chances of light traveling through 300 million meters with several molecules in each cubic meter is passes through, and not getting absorbed and re-emitted by ANY of them?

[/quote]Also, what's so special about 300,000 km anyway? You could shine a laser half a mile and measure the time it takes.[/quote]
I just picked that number because it's the number of km light travels in one second.

And - I really should have thought of this before - getting light to travel a given distance and timing it is not even the best way to measure its speed. You can actually do it better with an interferometer, which is a device that splits a light beam into two, sends them down different paths, and recombines them at a receiving screen. What you wind up seeing is a set of "fringes" which shift position as the length difference between the two paths changes, and the exact rate at which they shift position depends on the speed of light. So you can measure the shift and use it to calculate the speed.
How does the beam-splitting measurement work? Can you explain the logic of it so a layman can understand?

How would that be possible if every square meter contain several molecules? What are the chances of light traveling through 300 million meters with several molecules in each cubic meter is passes through, and not getting absorbed and re-emitted by ANY of them?
Rather high. At 10 atoms/m^3, any given 1000 nm square cross section path 300 million meters long contains about 0.003 atoms on average. And a photon's not guaranteed to interact with an atom it passes close to. If there were as many interactions as you suggest, the stars likely just wouldn't be visible, their light being spread in space and time (being deflected from their original trajectory, some being delayed more than others emitted at the same time) into a muddled mess that would smear their light out to an even, imperceptibly dim sky.

We can also measure how the speed of light changes in different conditions. It travels at very nearly c in sea level air, for most intents and purposes the difference is meaningless. It quite clearly approaches a finite and very similar velocity as the density of matter approaches zero. That velocity is c, exactly 299792458 m/s by definition. (the meter is now defined as the distance light travels in vacuum in 1/299792458 seconds)