If the critical angle for total internal reflection from a medium to vacuum is $45°,$ then velocity of light in the medium is,

Use the concept of critical angle in terms of the refractive index of a medium with respect to another medium, $\sin {\theta }_C=\frac{1}{\mu }$, 

$\Rightarrow \mu =\frac{1}{\sin {\theta }_C}=\frac{1}{\sin 45°}=\frac{1}{(1/\sqrt{2})}=\sqrt{2}$, now we know that the ratio of the speed of light in vacuum and speed of light in a medium is called the refractive index of the medium, $\mu =\frac{c}{v}\Rightarrow v=\frac{c}{\mu }=\frac{3\times {10}^8}{\sqrt{2}} \mathrm{m} {\mathrm{s}}^{-1}$.