\(\Delta=\frac{n_D-n_C}{n_0-1}=\frac{1}{30}\)

\(v_g=v_p(1+\frac{\lambda}{n}\frac{dn}{d \lambda}) \approx v_p(1+\frac{\lambda_D}{n_D}\frac{\Delta n}{\Delta \lambda})\)

\(\Delta n=n_C-n_F=\Delta(n_0-1)=\frac{1}{30}(1.5-1)=\frac{1}{60}\)

\(\Delta \lambda=\lambda_C-\lambda_F=656.3-486.1=170.2nm\)

\(v_g=\frac{c}{n_D}(1+\frac{\lambda_D}{n_D}\frac{\Delta n}{\Delta \lambda})=\frac{c}{1.5}(1+\frac{589}{1.5}\frac{1/60}{170.2})=\frac{c}{1.56}=1.92*10^8m/s\)