5. (20 points) Two mutually perpendicular rays, propagating in the same vertical plane, fall from air onto a horizontal glass surface. The refractive index of the glass $n=1.6$. The angle of refraction for the first ray $\beta=30^{\circ}$. Determine the angle between the refracted rays.
Answer: $52^{\circ}$.

Solution. The law of refraction for the first ray $\frac{\sin \alpha}{\sin 30^{\circ}}=1.6$. Therefore, the angle of incidence of the first ray $\alpha=53.13^{0}$. The angle of incidence of the second ray $\beta=90^{0}-53.13^{0}=$ $36.87^{\circ}$. The law of refraction for the second ray $\frac{\sin 36.87^{\circ}}{\sin \gamma}=1.6$. The angle of refraction of the second ray $\gamma=22^{0}$. In the end, we get the angle between the refracted rays $\beta+$ $\gamma=52^{0}$.