# Which fact is true about the speed and frequency of light?

I am totally stuck over this concept and google doesn't help.

First, We say that light's speed is constant for all colors in vacuum but different in all other media. Then which color's speed are we referring when we say that light's speed in that medium (like glass) is c divided by refractive index? Is it average of all or what?

Second, why do we say that frequency of light is constant when it changes media when we know that from red to violet, we have different frequencies and wavelengths (e.g. for violet it's 680-790 THz and 405-480 THz for red)?

• 1, Why do you think the refractive index is independent of wavelength? (buzzword: dispersion) 2. I don't understand what you're trying to ask here - the color we call "red" corresponds roughly to monochromatic light in the 405-480 THz range. What's the problem with that? Aug 10, 2020 at 22:09
• @ACuriousMind 1. I understand that refractive index depends upon wavelength but I am asking that which color's speed we refer to when we say that light's speed is X in glass/other medium because we'll have different speeds for all colors. 2. We always say that frequency of light is same for all colors i.e. doesn't change, only wavelengths change but we've different frequencies for all colors which I stated. Aug 10, 2020 at 22:21
• 1. Can you point to a source that talking about "light speed in glass" without specifying the wavelength it's talking about? 2. Sorry, I still don't understand - a light of 450 THz looks "red" to humans, so does a light of 460 THz (maybe a slightly "brighter red"). What's the problem with that? Aug 10, 2020 at 22:25
• @ACuriousMind Thanx, I understood the both parts. For second part, I was confused because we say that since wavelength of red is longer, everything else kept constant (like frequency), it will have greater speed. I confused "constant frequency" with "different frequency". We should also state that frequencies of different colors are also different (though constant) while comparing wavelengths i.e. there are two variables.That would make it clear. Aug 10, 2020 at 22:40
• @ACuriousMind, it's pretty common to find introductory materials that say "the index of refraction of glass is 1.5, and the index of refraction of water ice is 1.33" and so on, without any elaboration. Aug 10, 2020 at 22:56

Then which color's speed are we referring when we say that light's speed in that medium (like glass) is c divided by refractive index? Is it average of all or what?

First, if the speed of light changes for different frequencies, then we say the refractive index is also changing as a function of frequency. Speed is always $$c/n$$, but $$n$$ can be a function of frequency.

Sources that give a single number for the refractive index of some material are just presenting a simplified view of the situation.

If you look around, you can often find experimental data on what that functional dependence is.

For example, for BK-7 glass, the $$n(\lambda)$$, where $$\lambda$$ is the vacuum wavelength, function looks like this: You can see that the index only changes by about 1 or 2% over the visible wavelength band (~400-800 nm). We might easily just say $$n\approx 1.5$$, if we don't need to know about the small variations due to frequency.

On the other hand, if we want to find the chromatic aberration of a lens made from this glass, then we'll need to know how much $$n(\lambda)$$ varies before we can get started.

• Hey, I had read that the index of refraction is square root of $\epsilon_r$ where $\epsilon_r$ is the relative permittivity, which is a constant. Then how can n be a function of wavelength as it only depends upon the medium of travel Feb 17, 2021 at 15:50
• @Ruchi, it doesn't just depend on the medium, it depends on the medium and the wavelength. It might also (in birefringent materials) depend on the polarization of the beam. In extreme cases it might also depend on the intensity of the beam. Feb 17, 2021 at 18:51