Question

A 4. 9-mm-wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 20 ∘∘ above the horizon.

Answer 1

The depth of the swimming pool that is filled to the top is; 4 m

Snell's Law

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; brainly.com/question/10112549