# Speed of light and c

1. Jan 28, 2006

### dervast

Hi do u know if we increase the n in an optical fiber why the optical distance becomes bigger?

Now only this but why when we increase n the light goes slower and slower... How can we prove that? I know that n=c/u but still i need more explanation

2. Feb 11, 2006

### dervast

Can u plz help me with that?

3. Feb 11, 2006

### Meir Achuz

Showing u=-c/n usually takes several pages in an EM physics text.
You will just have to read some physics.

4. Feb 11, 2006

### Staff: Mentor

(I assume by "optical distance" you mean what English-language physics textbooks call the "optical path length".) It's because we define optical path length to equal the actual length times the index of refraction (n). We define it this way so that equal optical path lengths always contain equal numbers of wavelengths for the same frequency. This makes it easier to analyze interference in situations where light passes through different media with different n's.

The wavelength of light in a medium varies directly with n. The frequency stays the same while the speed varies inversely with n, which leads to your next question...

You have to analyze carefully the way the light interacts with electrons in the medium. Very broadly speaking, some of the incoming light is absorbed by electrons in the medium. The electrons radiate new light. The remaining incoming light and the new radiated light interfere in such a way that the resultant wave in the medium has a different phase velocity from the incoming light.

The above is the classical picture, in terms of classical electromagnetic waves. If you want a quantum-mechanical picture using photons, I'll let someone else try. I don't know enough quantum electrodynamics.

Last edited: Feb 11, 2006