Two transparent media A and B are separated by a plane boundary....

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, $\mu = \dfrac{c}{v}$.

So, for medium $A$, ${\mu}_{A} = \dfrac{c}{{v}_{A}} = \dfrac{3 \times {10}^{8}}{1 . 5 \times {10}^{8}} = 2$ and for medium $B$, ${\mu}_{B} = \dfrac{c}{{v}_{B}} = \dfrac{3 \times {10}^{8}}{2 \times {10}^{8}} = 1 . 5$

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

Using Snell's law,

${\mu}_{1}sini = {\mu}_{2}sinr$

$⇒ 2sini = 1 . 5\sin 90 ° ⇒ sini = \dfrac{1 . 5}{2} = 0 . 750 ⇒ i = \sin^{- 1}\left(0 . 750\right)$