Light passes from air into water at an angle of 40.0° to the normal.
The angle of refraction is smaller than the angle of incidence when light passes from a lower density medium (air = 1) to a higher density medium (water = 1.333)
The angle of refraction can be found using Snell's law given by
[tex]n_1\cdot\sin \alpha_1=n_2\cdot\sin \alpha_2[/tex]Where
n₁ = Refractive index of the air = 1
n₂ = Refractive index of the water = 1.333
α₁ = Angle of incidence = 40.0°
α₂ = Angle of refraction = ?
Let us substitute these values into the above equation and solve for α₂
[tex]\begin{gathered} n_1\cdot\sin \alpha_1=n_2\cdot\sin \alpha_2 \\ 1_{}\cdot\sin (40.0\degree)_{}=1.333\cdot\sin \alpha_2 \\ \sin \alpha_2=\frac{1_{}\cdot\sin (40.0\degree)_{}}{1.333} \\ \sin \alpha_2=0.4822 \\ \alpha_2=\sin ^{-1}(0.4822) \\ \alpha_2=28.9\degree \end{gathered}[/tex]Therefore, the angle of refraction is 28.9°
