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Chapter 34: Q 51 (page 992)

A 4.0-m-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. How deep is the pool?

Short Answer

Expert verified

The depth of the pool is 4.0 m

Step by step solution

01

Step 1. Given information is :Width of the swimming pool = 4.0 mBottom of the pool becomes completely shaded in the afternoon when sun is 20o above the horizonRefractive index of air n1 = 1Refractive index of water n2 = 1.33

We need to find the depth of the pool

02

Step 2. Using Snell's Law

As the Bottom of the pool becomes completely shaded in the afternoon when sun is 20o above the horizon, the ray refracting from the top edge of the pool do not reach the bottom of the pool after refraction as shown below :

Using snell's Law,

n1sinθ1=n2sinθ2sinθ2=n1n2sinθ1θ2=sin-1n1n2sinθ1θ2=sin-11.001.33sin70°θ2=44.95°

Let d be the depth of the pool. Then,

tanθ2=4.0mdd=4.0mtan44.95°=4.0m

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