For a transverse path of 1m for Cherenkov light emitted from a particle of normal incidence in fused silica, the time difference for $\beta$=1 and $\beta$=0.99 is only 61ps. However, due to dispersion both emission angle and speed of light in the medium are a function of the wavelength. For 300nm and 600nm photons the time difference is 0.5ns.

$ n_{group} = n_{phase} - \lambda dn_{phase}/d\lambda $

To calculate the propagation speed of the photons inside the dispersive medium the group velocity has to be used. The dynamic range of the corresponding group velocity refractive index is about 3 times larger than that of the normal refractive index.

The figure shows these velocities for fused silica.

-- KlausFoehl - 14 Sep 2005