How Does Refraction Help Calculate the Depth of a Pool?

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SUMMARY

The discussion focuses on calculating the depth of a pool using refraction principles. Given the refractive index of water (n=1.33) and an angle of 18 degrees above the horizon, participants explore how to apply Snell's Law to determine the depth of a 2-meter wide pool. A cross-section drawing is recommended to visualize the relationship between the angle of incidence and the refracted ray, which aids in deriving the depth mathematically.

PREREQUISITES
  • Understanding of Snell's Law and refraction principles
  • Basic geometry skills for drawing cross-sections
  • Familiarity with angles and trigonometric functions
  • Knowledge of the refractive index of water (n=1.33)
NEXT STEPS
  • Study Snell's Law and its applications in optics
  • Learn how to create geometric diagrams for refraction problems
  • Explore trigonometric functions related to angles and distances
  • Investigate real-world applications of refraction in various mediums
USEFUL FOR

Students studying physics, particularly those focusing on optics, as well as educators looking for practical examples of refraction in real-world scenarios.

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Homework Statement



The bottom edge of the opposite side of an in-ground pool (n=1.33) is just visible at an angle of 18 degrees above the horizon. If the pool is 2m wide what is the depth?


I think I'm stuck on trying to relate the refraction formulas as to determining depth. .. any tips or help?
 
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Make a cross-section drawing (of the pool and air above it) with a ray going from the bottom edge of the pool on one side, to the top edge of the pool on the other side. From there, draw the refracted ray. Can you now see how to find the depth from the angle and distance given?
 

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