(Solved): We wish to determine the depth D of a swimming pool filled with water (of index of refraction n ) b ...

We wish to determine the depth $D$ of a swimming pool filled with water (of index of refraction $n$ ) by measuring the distance $x$ from the near edge $A$ of the pools for which a person, tall of $h$, can just see the bottom of the pool's far edge $B$ (if the person stands at distance from the edge $A$ farther than $x$, she/he cannot see the bottom edge $B$ ). (a) Express sine the angle of incidence $\left(\sin \left({?}_1\right)\right)$ in term of $D$ and $w$. (b) Express sine the angle of refraction $\left(\sin \left({?}_2\right)\right)$ in term of $h$ and $x$. (c) Write Snell's law at $A$, and derive the equation giving $D$ in term of $w,h,x$ and $n$. (d) Calculate $D$ for $w=5.00m,h=1.70m,x=12.5m$ and $n=1.33$.