Question

How far (in cm) would light travel through diamond in 1.00 μs?

Answer 1

The speed of light in diamond is approximately

$$v= \dfrac{c}{n_d} = \dfrac{3\times 10^{10}cm/s}{2.42} \approx 1.24\times 10^{10}cm/s$$

(here $n_d = 2.42$ is the refractive index of diamond).

Thus, in time $t = 1\mu s = 10^{-6}s$ it will travel:

$$d = vt = 1.24\times 10^{10}cm/s\cdot 10^{-6}s=1.24\times 10^{4}cm$$

Answer. $1.24\times 10^{4}cm$.