Question

An underwater diver sees the sun$50°$above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver?

Short answer

The sun is $\sigma =31.25°$above the horizon to a fisherman in a boat above the diver.

Step-by-step solution

Determine the sun above the horizon to a fisherman in a boat above the diver:

The equation is,

$n_1\sin {\varphi }_1=n_2\sin {\varphi }_2$

The data are,

$\begin{array}{ll}{n}_1=1.00& n_2=1.33\\ {\varphi }_1=?& {\varphi }_2=40\end{array}$

Solve for$\sin {\varphi }_1$:

$\sin {\varphi }_1=\frac{n_2\sin {\varphi }_2}{n_1}$

Determine the Value ofσ:

${\varphi }_1={\sin }^{-1}\left(n_2\sin {\varphi }_2\right)$

Simplify:

${\varphi }_1=56.75°$

Substitute the value:

$\sigma =90-{\varphi }_1=31.25°$