Identify the angle of incidence and the angle of refraction when the ray passes from the transparent substance to the air:
The refractive index of the transparent substance is 1.09 and the refractive index of air is close to 1. Then:
[tex]\begin{gathered} 1\cdot\sin(x)=1.09\cdot\sin(65º) \\ \\ \Rightarrow\sin(x)=1.09\sin(65º) \\ \\ \Rightarrow x=\sin^{-1}\left(1.09\sin(65º)\right) \\ \\ \therefore x=81.0688...º \end{gathered}[/tex]
The angle α is complementary to the angle x. Then:
[tex]\begin{gathered} \alpha+x=90º \\ \\ \Rightarrow\alpha=90º-x=90º-81.0688...º=8.93...º \end{gathered}[/tex]
Therefore, the angle α is equal to 8.93º.
