Apparent Height in a Swimming Pool

In summary, the person swimming 0.95 m below the surface of the water sees an image of the diving board that is 6.00 m above them due to refraction. Using the equation (na/s)+(nb/s')=0 and plugging in the values given, the actual height of the diving board above the surface of the water is calculated to be -3.56 m, which is incorrect. Further attempts to solve for the image distance or the actual height also did not yield the correct solution. Help is needed to identify where the error may have occurred.
  • #1
rmcgovern
8
0

Homework Statement


A person swimming 0.95 m below the surface of the water in a swimming pool looks at the diving board that is directly overhead and sees the image of the board that is formed by refraction at the surface of the water. This image is a height of 6.00 m above the swimmer. What is the actual height of the diving board above the surface of the water?


Homework Equations


(na/s)+(nb/s')=0


The Attempt at a Solution


Rearranging the equation, I found s'=(nb*s)/-na. Plugging in nb=1.00, s=6.00m, and na=1.33, I found s'=-4.51, adding the depth of the swimmer, my final solution was -3.56m. This however is not correct. I also tried solving for s (which was actually my first attempt, although masteringphysics says the variable to solve for is s') to no avail. Any suggestions on where I may have gone wrong?
 
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  • #2
s is not the image distance from the surface of the water. 6.0 m is the sum of the image distance and the depth of the swimmer.
 
  • #3
ah, thank you for your help
 

1. What is apparent height in a swimming pool?

Apparent height in a swimming pool is the perceived height of an object when viewed from underwater. This can be affected by refraction, or the bending of light as it passes through the water.

2. Why does an object appear closer in a swimming pool?

An object appears closer in a swimming pool due to the phenomenon of refraction. As light travels from air to water, it changes speed and direction, making the object appear closer than it actually is.

3. How does the depth of the pool affect apparent height?

The depth of the pool can greatly affect the apparent height of an object. The deeper the pool, the greater the distance the light travels through the water, resulting in a larger amount of refraction and a greater change in the apparent height of an object.

4. Is apparent height the same for all objects in a swimming pool?

No, apparent height can vary for different objects in a swimming pool. The amount of refraction depends on the shape, size, and density of the object, as well as the angle at which it is viewed from underwater.

5. How can apparent height be calculated in a swimming pool?

Apparent height can be calculated using the following formula: AH = OH x (n1/n2), where AH is the apparent height, OH is the actual height of the object, and n1 and n2 are the refractive indices of air and water, respectively. This formula assumes that the object is viewed perpendicular to the water's surface.

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