Refraction in a Swimming Pool.

In summary: The pool is actually 4 meters deep.In summary, the conversation discusses the calculation of the depth of a swimming pool that is filled to the top and becomes completely shaded in the afternoon when the sun is 20 degrees above the horizon. The calculation involves using Snell's law and the index of refraction of air and water. The result is that the pool is approximately 4 meters deep.
  • #1
physicsstudent14
13
0

Homework Statement


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 degrees above the horizon. How deep is the pool?

Homework Equations


Snell's law
(n1)sin(x1) = (n2)sin(x2)
Index of Refraction of Air = 1
Index of Refraction of Water = 1.33

The Attempt at a Solution



I drew a picture with the sun 20 degrees above the horizontal, which meant that x1 is 70 degrees relative to the normal. I know n1 is the index of refraction of Air, 1. I solved for x2, using n2 = index of refraction of water = 1.33.

(n1)sin(x1) = (n2)sin(x2)
(1)sin(70) = (1.33)sin(x2)

I solved for x2 and got 45 degrees for the light angle in water relative to the normal.

Now that I know x2, I tried to solve for the depth of the pool d by using the width w = 4.0 m.

I got tan(x2) = (4 m)/d
d = (4 m)/tan(45) = 4 m.

I don't think my result makes sense. It seems too simple. How am I supposed to figure out the depth of the pool? I've never experienced a problem where the bottom was completely shaded. Can someone please explain to me what I'm doing incorrectly? Thanks for your help.
 
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  • #2
You have solved the problem correctly--whether you know it or not. (Correct your units--it's meters, not centimeters.)

Imagine the sun is coming from the right, hitting the water. The light refracts in accordance with Snell's law. Now consider the light that just hits the right-most section of the pool water. If that light bends enough so that it hits the wall of the pool, not the bottom, then surely none of the other light will shine on the pool bottom. (Draw yourself a picture and you'll understand it better.) Make sense?
 
  • #3
edit: Doc Al beat me to it.
-------------
Everything is fine, all the way to (4m)/tan(45 degrees)
How'd you get 4 centimeters?? tan(45 degrees) = 1

Otherwise, everything is good.
 
  • #4
Thanks I think I understand it now. I just messed up on the units.
 

Related to Refraction in a Swimming Pool.

1. What is refraction in a swimming pool?

Refraction in a swimming pool is the bending of light as it passes from one medium (air) to another (water) due to the change in the speed of light. This phenomenon is what causes objects to appear distorted or shifted when viewed from above the water's surface.

2. Why does refraction occur in a swimming pool?

Refraction occurs in a swimming pool because light travels at different speeds in different mediums. When light enters the water, it slows down, causing it to bend and change direction. This bending of light is what causes the familiar "shimmering" effect in swimming pools.

3. How does the depth of the water affect refraction in a swimming pool?

The depth of the water plays a significant role in refraction in a swimming pool. The deeper the water, the more pronounced the refraction will be. This is because the light has further to travel and is subject to more changes in speed, resulting in a more significant bending effect.

4. Can refraction in a swimming pool be corrected?

No, refraction in a swimming pool cannot be corrected. However, the effect can be minimized by viewing objects from directly above the water's surface, where the light is not passing through as much water and is therefore subject to less bending.

5. How does temperature affect refraction in a swimming pool?

Temperature can affect refraction in a swimming pool because it affects the density of the water. Warmer water is less dense than colder water, causing light to travel through it at different speeds and resulting in a different amount of bending. This can cause a change in the appearance of objects in the pool as the temperature changes.

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