Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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.

Sagot :

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; https://brainly.com/question/10112549

View image AFOKE88
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.