# Frequency dependence of the speed of light in air

According to this link, the speed of light of different colors in a medium should be different. But if the refractive index of light in air is 1 then this means that the speed of light in air and vacuum should be the same. Could anyone help me out here?

Thanks

• The refractive index in air is 1.000293, not 1. Mar 3, 2015 at 11:30

You have two different concepts intertwined in your question. You begin by asking about the speed of light in a medium varying with color (i.e. wavelength). This phenomenon is called dispersion and it is present in all materials including air. Dispersion shows up in many places in the field of optics, but the case you are probably most familiar with is the separation of white light into its individual colors by a prism.

The other, somewhat unrelated concept that you ask about is the fact that the index of refraction of air is different from that of vacuum. In reality, the index of refraction of air is slightly different than vacuum, but in practice this small difference can often be neglected. Even air has some dispersion (see below), but not enough to separate the light from the sun into distinct colors like a prism.

It is true in general that the speed of light in a medium will depend to some extent on the wavelength/frequency of the light itself, but in most (not all) everyday situations this is not apparent or important, and makes the theory of optics much easier mathematically.

As for the refractive index of air, it is not quite 1, but slightly larger, 1.0003 IIRC, so although we can approximate this as 1, actually light will travel slightly slower in air than it would in a vacuum.

As mentioned by others so far, the index of refraction ($$n$$) of air is not identically equal to 1, but is in fact $$n=1.000293$$. For many every day situations this small difference is negligible; however, it is possible to observe that light does in fact change speed when changing mediums from a vacuum to air.

At sunrise and sunset, the sky appears red and orange near the horizon. This is due to the refraction of sunlight as it enter's the earth atmosphere from space. When the sun is low on the horizon, light travels a greater distance in the atmosphere, and this effect is most noticeable. It's worth mentioning as well, before someone comments and points out, that in this situation the index of refraction of air actually changes throughout the atmosphere, because air becomes more dense closer to the surface of the earth. At any rate though, this still demonstrates that for air, $$n\not=1$$

Photo courtesy of gohawaii.com