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 $

fused silica - n_phase and n_group 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
Topic revision: r2 - 2006-02-02, CarstenSchwarz
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