Answer
$2.46\times10^{8}m/s$
Work Step by Step
Recall that index of refraction $n= \frac{sin i}{sin r}=\frac{c}{v}$
where i is the angle of incidence, r is the angle of refraction, c is the speed of light in air and v is the speed of light in the material.
Thus, we find:
$\frac{sin 63.0^{\circ}}{sin 47.0^{\circ}}=\frac{3.00\times10^{8}m/s}{v}$
$⇒v=\frac{3.00\times10^{8}m/s\times sin 47.0^{\circ}}{sin 63.0^{\circ}}$
$=2.46\times10^{8}m/s$
