The frequency of a light wave in a material is $2\times {10}^{14}$ Hz and wavelength is 5000 $\stackrel{\mathrm{o}}{\mathrm{A}}$. the refractive index of material will be

Velocity of light waves in material is

$\begin{array}{l}\mathrm{v}=\nu \lambda ....\left(\mathrm{i}\right)\\ \mathrm{Refractive}\mathrm{index}\mathrm{of}\mathrm{material}\mathrm{is}\mathrm{\mu }=\frac{\mathrm{c}}{\mathrm{v}}..\left(\mathrm{ii}\right)\\ \mathrm{where}\mathrm{c}\mathrm{is}\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}\mathrm{or}\mathrm{air}.\\ \mathrm{or}\mathrm{\mu }=\frac{\mathrm{c}}{\mathrm{v\lambda }}...\left(\mathrm{iii}\right)\\ \mathrm{Given},\mathrm{v}=2\times {10}^{14}\mathrm{Hz}\\ \mathrm{\lambda }=5000\stackrel{\mathrm{o}}{\mathrm{A}}=5000\times {10}^{-10}\mathrm{m},\\ \mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}\\ \mathrm{Hence},\mathrm{from}\mathrm{Eq}.\left(\mathrm{iii}\right),\mathrm{we}\mathrm{get}\\ \mathrm{\mu }=\frac{3\times {10}^8}{2\times {10}^{14}\times 5000\times {10}^{-10}}=3.00\end{array}$