Question #43219

A quasi-monochromatic light pulse with central angular frequency $\omega_0$ propagates through a dispersive glass slab of thickness $L = 1.50 \text{ m}$. The dispersion relation for the glass is given by $k(\omega) = \frac{\omega}{c}(n_0 + \alpha \omega^2)$, where $k$ is the wave number, $c = 3.0 \times 10^8 \text{ m/s}$ is the speed of light in vacuum, $n_0 = 1.50$, and $\alpha$ is a positive dispersion coefficient such that $\alpha \omega_0^2 = 0.020$. At $t=0$, the centroid of the wave packet and a specific phase front (crest) exactly coincide at the entry surface of the slab. Assuming the medium outside the slab is vacuum, what is the spatial separation between this specific phase front and the centroid at the exact instant the centroid reaches the exit surface of the slab?