Question

An underwater scuba diver sees the Sun at an apparent angle of 43.5° above the horizontal. What is the actual elevation angle of the Sun above the horizontal?

Answer 1

According to Snell's law,

`n_1\sin \theta_1=n_2\sin \theta_2`

The refrative index of water is 1.333 and the refractive index of air is 1.

Substitute the known values,

`\begin{gathered} (1)\sin \theta_1=(1.333)\sin 43.5^(\circ) \\ \sin \theta_1=(1.333)(0.688) \\ \theta_1=\sin ^(-1)(0.917) \\ =66.5^(\circ) \end{gathered}`

The angle above the horizontal is calculated as,

`\begin{gathered} \theta_1=90^(\circ)-66.5^(\circ) \\ =23.5^(\circ) \end{gathered}`

Thus, the actual elevation angle of Sun above the horizontal is 23.5 degree.