Let the $x - z$ plane be the boundary between two transparent media. Medium ${\rm{1}}$ in $z\,\, \ge \,\,0$ has a refractive index of $\sqrt 2 $ and medium ${\rm{2}}$ with $z\,\, < \,\,0$ has a refractive index of $\sqrt 3 $. A ray of light in medium ${\rm{1}}$ given by the vector ${\bf{A}} = 6\,\sqrt 3 \hat i + \,\,8\sqrt 3 \hat j\,\,-\,\,10\,\hat k$ is incident on the plane of separation. The angle of refraction in medium ${\rm{2}}$ is