Geometrical Optics

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