From the given expression: $\mathit{\omega }=1.5\times {10}^{11}$ rad/s and $\mathit{k}=\mathit{\alpha }$. The speed of light in glass with refractive index n = 1.5 is:
$\mathit{v}=\frac{\mathit{c}}{\mathit{n}}=\frac{3\times {10}^8}{1.5}=2\times {10}^8\mathit{m}∕\mathit{s}$
Using the relation $\mathit{v}=\frac{\mathit{\omega }}{\mathit{k}}:$
$2\times {10}^8=\frac{1.5\times {10}^{11}}{\mathit{\alpha }}$
$\mathit{\alpha }=\frac{1.5\times {10}^{11}}{2\times {10}^8}=0.75\times {10}^3=7.5\times {10}^2{\mathit{m}}^{-1}$
The value of α is $7.5\times {10}^2{\mathit{m}}^{-1}$.