# Laser, color and speed of light

Mr.Ed

## Main Question or Discussion Point

Anyone knows any good websites, books, resources for information about how the color of a laser might affect the velocity og the light wave projected by the laser ?

Any help is appreciated.

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mathman
Please try to clarify what you are getting at. The speed of light does not depend on color.

Originally posted by mathman
Please try to clarify what you are getting at. The speed of light does not depend on color.
It does if the light is not in a vacuum.

That's called dispersion

Originally posted by Dave
It does if the light is not in a vacuum.
and has to do with the fact that the speed of EM waves is defined by the index of refraction for different materials.

Mr.Ed
Extra Information

well the instructor gave us this problem ( Im a college freshman, so they dont give us much information)

" Laser, which use light rays of set wavelenghts(colors), are in constant use in our world. Determine whether the color of a laser affects the velocity of the light wave projected by the laser."

maybe i phrase the question wrong, the first time, but this was all the information he gave us for this problem. Although a yes or no answer helps, im looking to understand the problem as in how, if they are, the light wavelenghts are affected. Any references, books, websites that could give me some information for this would help.

Thanks for the quick replies and all help in advance.

Homework Question

Mr. Ed:

The question is, even in its original form, a bit confusing. There are a few important concepts that may help you answer the question. One is the concept known as the "index of refraction", and another is that of a "dispersion relation". I will begin by addressing your question in terms of everyday visible light (such as that comming from the sun, or from an incandescent light bulb).

Firstly, the speed (or "group velocity") of light in a vacuum (i.e. no air, no water, nothing) is absolutely constant. In fact, it has now become a standard (we have defined our unit system using it) which prevents people from measuring its value more accurately (ask if this confuses you). Its value is exactly 2.99792458 x 10^8 m/s.

When light travels in a medium other than air, for example water or glass, its speed inside the medium decreases. By how much does this decrease? That depends on something called the index of refraction (given the symbol, n) which is a property of the medium. So, glass, air, and vacuum all have different indecises of refraction. Here are a few:

n(vacuum) = 1
n(air @ standard temperature and pressure) = 1.00029
n(diamond) = 2.417
n(glass) = 1.5

Such indecises are usually tabulated in textbooks as being numbers, HOWEVER, in reality, the index of refraction is actually a function of wavelength - this is called a DISPERSION RELATION.
i.e.

(!= means not equal to)

n != constant
n = n(&lambda;)

The numbers I have posted above are given for a specific wavelength, so they give you an idea of how the medium responds to visible light.

So, what are the implications of this DISPERSION RELATION? When light is travelling through a medium (i.e. not in vacuum), if it has different spectral components (i.e. is composed not of a single wavelength, but a distribution of wavelengths) then each component will travel at a different speed.

Having said that, "[Does] the color of a laser affect the velocity of the light wave projected by the laser"?

Well, if the laser is in a vacuum, then the answer is "No" because there is no dispersion relation (i.e. all wavelengths travel at the same speed). If it is in air, then the answer, technically, is "Yes. But very slightly."

If you are wondering why I said very slightly, it is because a red 632 nm (Helium-Neon), infrared 1064 nm (Nd:YAG), and blue 442 nm (Hedlium-Cadmium) laser all have similar wavlengths and the dispersion in air is extremely small.

As a side note, what makes a laser so special (and useful) as opposed to that coming from a light-bulb? This is very important to know. The answer lies in the following properties of a laser:

(in no particular order)
1. LASER light is highly directed (i.e. unidirectional). This means that all of the light energy is being concentrated into a very small solid angle instead of being distributed isotropically (isotropically means "the same in all directions").

2. LASER light is coherent. This a tougher to understand than (1). This means that all photons are emitted IN PHASE with one another. Because light is wave-like, you can ascribe to it a phase (just like you can a water wave). What happens when two water waves collide? If they are IN PHASE, they interfere CONSTRUCTIVELY. If they are exactly OUT OF PHASE, they interfere DECONSTRUCTIVELY. So, laser light, because it is emitted coherently, is a very "economical" source of light. Light isn't wasted because different components are interfering destructively. This results in large intensities.

3. LASER light is monochromatic. All of the light emitted from a laser is compressed within a very small band of wavelengths. Although the word "mono" implies one, in reality, there is still a distribution of wavelengths over which a laser emits light. However, most laser sources emit light with linewidths << 1 nanometre.

Mr.Ed
Thanks for the explanation , it did help me understand the subject a whole lot better.

Thanks again.

GAB
hey

hey guys, i read all through this thread, and i dunno if im at the same school as mr.g. but i got the same question
"PROBLEM

Lasers, which use light rays of set wavelenghts (colors), are in constant use in our world, in everything from surgery to supermarket checkout scanners.
Execute the necessary research to determine whether the color of a laser affects the velocity of the light wave projected by the laser"

now i dont claim to be smart in this field at all yet, i just started college...so sdeliver645, i didnt understand a word you said, sorry but can someone please explain this to me in a way i can understand?

GAB:

The answer depends on the medium the light is travelling in.

Blue light and red light in outer-space travel at the same velocity (no dispersion). Blue light and red light in air travel at very slightly different velocities; this is called dispersion.

The question is not unique to lasers, but to light in general.

GAB
sdeliver645

i dont know if in that question they wanted me to explain how to determine it which would be a messed up question to ask someone in the first quarter and to have them do by themselves....i think ill be able to just say yes or no....i was looking at ur response to mr. g about if its in a vacuum then the answers no, if its in air then yes...would u mind if i quoted you for my answer...because it tells me to give the source where i found the info..i would really appreciate it, thanks for trying to explain

russ_watters
Mentor
Sounds like a trick question to me - medium or not (thats the trick) the answer is NO.

To expand, light doesn't really travel through a medium - it only travels through a vacuum. And only ever at C. Travel through a medium is an AVERAGE speed that is dependent on absorption and re-emission. But between instances of absorption and re-emission it travels in a vacuum and at C.

It is of course possible that your prof is talking about light in the macroscopic sense. Then there are differences. But for a college course, it shouldn't be oversimplified like that.

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Nereid
Staff Emeritus
Gold Member
fibre optics?

Maybe the context includes fibre optics and the use of lasers and optical fibres in telecommunications (for example)?

Clarification

GAB:

I would like to clarify something that russ_watters said. I will mention that everything russ_watters said is quite correct. What I would like to point out is that if you were to measure the time it takes a laser beam to travel through, say, a 1 m distance of water, you would NOT get t=(1 m)/(3x10^8 m/s). So, what does this mean? What speed does light travel through the water?

The answer is that, just as russ_watters mentioned, in between water molecules light travels at 3x10^8 m/s. However, light is temporarily "stored" when it interacts with a molecule. So, if you were to measure the time it takes it light to travel down an optical fiber, it would NOT correspond to the speed of light (2.99792458x10^8 m/s). It would correspond to the ratio c/n, where n is a wavelength-dependent parameter. That means that if you send a white-light pulse down and optical fiber, you will get out a blurred-out distribution of different colours (for visible light, colours will be sorted almost linearly by wavelength). This, as previously mentioned, is called dispersion.

About quoting me, it is kind of inappropriate, but you are quite welcome to. You only quote personal correspondence if the information is not available elsewhere, such as unpublished results or a controversial opinion. I would suggest you quote a physics text, such as:

Wolfson and Pasachoff, Physics with Modern Physics for Scientists and Engineers, Addison Wesley, 1999.

or

Serway and Faughn, College Physics, Thomson, 2003.

Good luck!

GAB
damn i wish i could be as smart as you guys some day, hopefully my school does it to me lol.....thanks for all the help guys, it really made me understand, and whats funny about this question....this isnt even a hard class....its a problem solving class lol

Cool article

You flatter us...

Here is a nice article from MIT's Technology Review. It is based on a recent article in Science. Read it.

It is a intended for a general audience.

It is called something like "Crystal Stops and Speeds Up Light"

http://www.technologyreview.com/articles/rnb_100803.asp [Broken]

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Let me Guess???

Mr. ED are you going to ITT. I have the same problem solving class with the same dang question...
And no it does not say whether its with or without a vaccum.
so what is a good base answer. i would say with out a vaccum.
:tongue: