# Phase and signal velocity of light inside a medium

1. Jan 1, 2009

### lightarrow

Don't know if this is the correct forum.

While we know that light's phase velocity in a linear medium with refration index n is c/n, what can we say about signal's velocity? If I switch on a laser inside the medium (let's say glass) at t = 0, when will the first photon arrive to a detector placed L metres away? At t = L/(c/n) or at t = L/c or else?

2. Jan 1, 2009

### clem

If n does not vary too rapidly with wavelength, a pulse of light will travel with the group velocity $$v_g=\frac{\partial\omega}{\partial k}$$.

3. Jan 3, 2009

### lightarrow

Do you know the dispersion relation $$\omega(k)$$ or $$n(\lambda)$$ in the visible range for a common glass?

4. Jan 3, 2009

### Cthugha

This depends a bit on the kind of glass you have.

Have a look at the download page of Schott glasses (a rather large company dealing with glasses and optical filters):

Techical information 29 has some basic definitions and shows refraction index versus wavelength for fused silica glass. In the top of the page there is also a link to a glass map leading to an overview of some commonly used glasses, where n versus wavelength is given for 20 or so standard wavelengths for each filter. Maybe look for BK7. This is also a very common glass.

5. Jan 3, 2009

### lightarrow

So, you agree that signal velocity = group velocity for common glasses in the visible range?

6. Jan 3, 2009

Yes.

7. Jan 5, 2009

### lightarrow

Thanks to both (but you are the same person?)