= Transit and pulse evolution
Taking $L=1.00\,\mathrm{cm}$ as the distance travelled in the medium, the narrowband <group delay> is
$$
\boxed{t_g=L/v_g=8.76\times10^{-11}\,\mathrm s=87.6\,\mathrm{ps}}.
$$
If $1\,\mathrm{cm}$ denotes a slab thickness measured normal to the interface instead, the central ray travels $L/\cos17.80^\circ$, giving about $92.1\,\mathrm{ps}$. The coordinate-mixed velocity above would give $89.3\,\mathrm{ps}$ for a $1\,\mathrm{cm}$ path; it should not replace the consistent calculation silently.
The pulse envelope travels at the local <group velocity>, while individual carrier crests move at the <phase velocity>. In general, variation of <group velocity> across the pulse spectrum produces different delays, temporal broadening and chirp. Absorption can reshape the spectrum and envelope as well. The refraction data also show wavelength-dependent angles, so a finite-width incident beam acquires spatial separation of its spectral components. The supplied first derivative determines the central delay but does not specify a pulse duration, absorption spectrum or reliable second derivative of the <dispersion relation>; it therefore does not determine a numerical broadening, or its sign. If propagation <phase> is effectively linear across a sufficiently narrow spectrum, the leading approximation is a delayed pulse with unchanged shape.
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