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(λ)
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 traveling 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.
