The frequency of a light wave in a material is 2 × 10^ 14 ~Hz and...

Velocity of light waves in material is $v=\mathrm{v} \lambda\ldots(i)$ Refractive index of material is $\mu=\frac{c}{v}\ldots(ii)$ where $c$ is speed of light in vacuum or air. or $\mu=\frac{c}{v \lambda}\ldots(iii)$ Given, $\quad v=2 \times 10^{14} \mathrm{~Hz}$, $$\begin{aligned} \lambda & =5000 Å=5000 \times 10^{-10} \mathrm{~m}, \\ c & =3 \times 10^8 \mathrm{~m} / \mathrm{s} \end{aligned}$$ Hence, from Eq. (iii), we get $\mu=\frac{3 \times 10^8}{2 \times 10^{14} \times 5000 \times 10^{-10}}=3.00$