The depth of the swimming pool that is filled to the top is; 4 m
I have attached a schematic diagram showing this question.
The correct width of the pool is 4 meters. Thus; w = 4 m
Incident Angle; θ₁ = 20°
A right angle is 90° and so the angle θ₂ is calculated from;
θ₂ = 90° - θ₁
θ₂ = 90° - 20°
θ₂ = 70°
We can use snell's law formula to find θ₃.
Thus;
n₁sinθ₂ = n₂sinθ₃
where;
n₁ is refractive index of air = 1
n₂ is refractive index of water = 1.33
Thus;
1*sin 70 = 1.33*sin θ₃
sin θ₃ = (sin 70)/1.33
Solving this gives;
θ₃ = 44.95°
By usage of trigonometric ratios we can find the depth of the pool using;
w/d = tan θ₃
Thus;
d = w/(tan θ₃)
d = 4/(tan 44.95)
d ≈ 4 m
Read more about Snell's Law at; https://brainly.com/question/10112549
