Final answer:
The student's question involves Group Delay Dispersion (GDD) and the temporal extent of a light pulse in glass. Exact calculations cannot be made without specific wavelengths. However, GDD refers to pulse broadening due to refractive index changes with frequency and affects the temporal extent of the pulse.
Step-by-step explanation:
The student's question about the propagation of an ultrafast pulse of light through glass involves calculating the Group Delay Dispersion (GDD) and determining the temporal extent of the pulse after it enters a material with a variable refractive index. While the answer requires precise calculations and knowledge on the relationship between refractive index, wavelength, and the speed of light in a medium, the question provided does not include sufficient information to perform these calculations (such as the actual wavelength of the light). Therefore, a general answer will be provided explaining the concepts involved.
Group Delay Dispersion (GDD) refers to a pulse-broadening effect where different frequency components of a pulse travel at different speeds due to the refractive index's dependency on frequency. The GDD increases with the length of the propagation medium and with the change in refractive index with frequency (or wavelength).
The temporal extent of the pulse after traveling through 1 cm of glass depends on the initial pulse width, the refractive index of glass, and the GDD. A more significant GDD usually leads to a broader pulse. The sketches for GDD and temporal extent would depict this effect but cannot be provided in text format.