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Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is different. On the other hand, when talking about the speed of light, I've always heard only one value. Why is it so? Shouldn't it be like the red color's speed must be way higher (or lower) than, say, the purple color's speed? I am quite confused here.

(Sorry if my question is too foolish, but it has bugged me for years and I was quite bad at physics at school and have never touched it since I finished school)

Qmechanic
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brilliant
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    Great question - for a very long time, we weren't sure, even after we became quite sure the speed of light is finite in the first place. Don't be ashamed of questions that have a simple, well known answer - that doesn't make the question bad. – Luaan Dec 09 '19 at 10:27
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    Great question, but I want to suggest one modification: do frequencies differ in terms of speed? Newton, in Opticks, says (I'm quoting from memory here) "Strictly speaking, the rays are not colored," and then makes the point that the rays of light have some property (as yet undetermined) that causes us to perceive them differently, and we call these different perceptions "color." In other words, frequency is a physical phenomenon; color is a perceptual one (and things like the surround-effect show that it's not a very stable perceptual one, either!). – John Dec 09 '19 at 16:18
  • Possible duplicates: https://physics.stackexchange.com/q/129382/2451 and links therein. – Qmechanic Dec 09 '19 at 20:12
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    @Qmechanic can you please reopen? The answers (on the other question) are really nice, in technical detail about electron (harmonic) oscillation, and the classic and QM quantities (lattice structure like slit experiment) of glass (prizm), though they do not have a simple explanation about why it is not wavelength dependent in vacuum and why it is wavelength dependent in media. – Árpád Szendrei Dec 09 '19 at 20:31

5 Answers5

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The speed of light is always c in vacuum, when measured locally, independent of the wavelength.

Though, in a medium, the index of refraction is n=c/v.

Speed of different em radiation in a medium

Now if the index depends on the wavelength, then different wavelength (color) light has to have different speeds in the medium.

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light travels through the material. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.

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

So the answer to your question is, that in vacuum, the different wavelength light all travel always at speed c when measured locally, but in a medium, the speed of light is dependent on its wavelength.

Árpád Szendrei
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    As a side note: The differing speeds at different frequencies through a medium (like water) is the reason we have rainbows. – Arthur Dec 09 '19 at 11:05
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    What do you mean by „when measured locally“? – ilmiacs Dec 09 '19 at 12:42
  • @ilmiacs It means the speed is local, not global. This is an important distinction in relativity that takes a lot of explaining. But an example of why this matters: if you wave your hand in front of a flashlight aimed at the moon, your shadow can seem to move across the moon's surface at a speed $>c$, but this is legal because it's a global speed. – J.G. Dec 09 '19 at 12:58
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    this has made me suddenly realize - in reality there are no vacuums anywhere – Fattie Dec 09 '19 at 13:16
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    @Fattie Also, what we call the speed of light in a vacuum is a fundamental constant even if there is no light and no vacuum. – user126527 Dec 09 '19 at 13:18
  • quite right, @JollyJoker what I had in mind is, astronomers/cosmologists as a commonplace consider the very thin mediums between galaxies as something not nothing; I wonder if they have to worry about the differing speeds in such a medium? – Fattie Dec 09 '19 at 13:19
  • @Fattie Probably not much. I remember a GRB that put very low limits on a frequency-dependent speed of light since a single photon was detected with such a high energy compared to the rest at almost the same time. Maybe the phrase "frequency-dependent speed of light" would give some hits if you want more. – user126527 Dec 09 '19 at 13:22
  • Another example that speed of light inside a transparent medium (not in a vacuum) often demonstrated to schoolchildren is a prism. A prism separates the colors because the speed of light (the "refraction index") is slightly different for the different colors (wavelengths), so their direction changes differently for the different colors. But this is not because of the properties of light itself, but rather its interaction with the medium it is traveling through. – Nadav Har'El Dec 09 '19 at 14:21
  • @Fattie Depends on how large a volume of space you're referring to. The densest outerspace nebula is orders of magnitude less dense (1,000,000 atoms per cubic centimeter) than the best vacuum ever made in a lab (1,000,000,000,000 atoms per cubic centimeter). On the low-end of the spectrum...well, it gets pretty small. ;) – Draco18s no longer trusts SE Dec 09 '19 at 16:17
  • Drac - yes, of course! But space is awfully big. For example it's commonplace for cosmologists to figure the temperature, extinguishing factors, and other properties of even the inter-supercluster medium. (!) I wonder if those ultra-thin mediums make a rainbow (as in the children's example Nadav mentions!) – Fattie Dec 09 '19 at 17:08
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The speed of a wave is given by:

$$c=f\lambda$$

Where $c$ is the speed of the wave, $f$ is the frequency and $\lambda$ is the wavelength. You're right that different colours have different frequencies, but light with a lower frequency has a longer wavelength, in other words if $\lambda$ goes up then $f$ has to come down so they cancel each other out and the speed stays constant.

Charlie
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Imagine that you have a great big loudspeaker on top of a mountain, with a switch that makes the loudspeaker cone jump into one of two positions. When you flick the switch down, the cone jumps forwards and sends out a positive pulse, and when you flick it up, the cone jumps back again and sends out a negative pulse. The speed at which your standard pulses move through the air depends on things like air temperature and density.

Sound travels at about 300 metres per second. Two pulses makes a wavecycle. If you change the switch position once every ten minutes, you have a squarewave signal with a 1/300hz frequency. If you flick it once a second you have a signal with a 1/2 Hz frequency. There's no obvious reason why the individual pulses would move at a different speed just because there's another pulse behind them or ahead of them maybe a kilometre away. The pulse speed doesn't care whether you flick the switch once a minute, once a month, or once a year.

So there's a range in which the signal speed is independent of the frequency.

Frequency only really starts to become an issue if the frequency is high enough and the wavelength small enough to interfere with some scale of structure in the medium, or if the waves are close enough to each other to start interacting, or if the energy transmitted is great enough to start altering the properties of the medium (like, your soundwaves start heating up the air).

For light in a vacuum, you're only supposed to start getting frequency-dependencies if the frequencies are so absurdly high (like, ultra-ultra-hard gamma rays) that the energies start distorting spacetime and/or creating particles so that you no longer have a vacuum. But even if that starts happening, it's going to tend to affect all frequencies.

Eric Baird
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No, they are related by the formula

$$c_0 = f \cdot \lambda$$

with speed of light in vacuum $c_0$, frequency $f$ and wavelength $\lambda$.

A change in frequency demands an anti proportional change in wavelength and vice versa, since the speed is constant. It is not possible to change the frequency and leave the wavelength constant.

This is quite intuitive because the frequency is the timescale how often a wave peak will pass in a given time. But of course this depends on the wavelength:

enter image description here

Image source

infinitezero
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The speed of light is completely independent of the wavelength, provided the medium is vacuum or air.

But In other medium, like water or glass the speed Of light of different wavelengths decrease differently. This phenomenon is known as Dispersion Of Light

In a medium the Speed Of red light is maximum and that of violet is minimum.

This is how we see the colours of the rainbow.

Rory Alsop
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Saikat Das
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    I disagree about air. This is not a special medium, so also in air you have a difractive index and therefore speed which is dependent on wavelength: "For visible light, refraction indices n of most transparent materials (e.g., air, glasses) decrease with increasing wavelength λ" from Wikipedia – elzell Dec 09 '19 at 11:13
  • The formatting on this seems very excessive to me, and makes it harder to read. There's no need to use this much caps, italics and bold; nor does the emoji help make things clear. – JMac Dec 09 '19 at 15:05