Apparent Height in a Swimming Pool

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SUMMARY

The discussion focuses on calculating the actual height of a diving board above the surface of a swimming pool, given that a swimmer is 0.95 m below the surface and sees the board's image at 6.00 m above them. The refraction equation used is (na/s) + (nb/s') = 0, where na is the refractive index of water (1.33) and nb is that of air (1.00). The incorrect calculation led to a final result of -3.56 m, indicating a misunderstanding of the image distance and swimmer's depth. The correct approach requires recognizing that the total height includes both the image distance and the swimmer's depth.

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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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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.
 
ah, thank you for your help
 

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