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 $n=1.5$. The angle of refraction for the first ray $\beta=25^{\circ}$. Determine the angle between the refracted rays.
Answer: $56^{\circ}$.

Solution. The law of refraction for the first ray $\frac{\sin \alpha}{\sin 25^{\circ}}=1.5$. Therefore, the angle of incidence of the first ray $\alpha=39.34^{\circ}$. The angle of incidence of the second ray $\beta=90^{\circ}-39.34^{\circ}=$ $50.66^{\circ}$. The law of refraction for the second ray $\frac{\sin 50.66^{\circ}}{\sin \gamma}=1.5$. The angle of refraction of the second ray $\gamma=31^{\circ}$. The angle between the refracted rays: $\beta+\gamma=56^{\circ}$.