Refractive index $\left(\mu \right)$ in terms of speed of light $\left(c\right)$ in vacuum and wave speed $\left(v\right)$ in medium is given by, $\mu =\frac{c}{v}$.

So, for medium $A$, ${\mu }_A=\frac{c}{v_A}=\frac{3\times {10}^8}{1.5\times {10}^8}=2$ and for medium $B$, ${\mu }_B=\frac{c}{v_B}=\frac{3\times {10}^8}{2\times {10}^8}=1.5$

For critical angle, angle of refraction $r=90°$.

Using Snell's law, 

${\mu }_1\sin i={\mu }_2\sin r$

$$\begin{gathered} \Rightarrow 2\sin i=1.5\sin 90° \\ \Rightarrow \sin i=\frac{1.5}{2}=0.750 \\ \Rightarrow i={\sin }^{-1}\left(0.750\right) \end{gathered}$$