If the critical angle for total internal reflection from a medium...

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

$⇒ \mu = \dfrac{1}{sin{\theta}_{C}} = \dfrac{1}{\sin 45 °} = \dfrac{1}{( 1 / \sqrt{2} )} = \sqrt{2}$, 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, $\mu = \dfrac{c}{v} ⇒ v = \dfrac{c}{\mu} = \dfrac{3 \times {10}^{8}}{\sqrt{2}}m{s}^{- 1}$.