Answer to Question #171483 in Optics for Richard

Question

The diver sees the sun at an angle of 50 ° above the horizon. Find the angle at which a fisherman in a boat on the surface of the water sees the Sun, again relative to the horizon. The refractive index of water is 1.33.

Answer 1

θ_γ = 90 – 50 = 40º

$n_{air}sinθ_i = n_{water}sinθ_γ \\ 1 \times sinθ_i = 1.33 sin40º \\ θ_i = sin^{-1}(1.33 \times sin40º) \\ = 58.75º$

φ = 90 – 58.75 = 31.25º

31.25º is the angle at which a fisherman in a boat on the surface of the water sees the Sun, again relative to the horizon.