Actual vs percieved depth. optics question

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SUMMARY

The discussion centers on calculating the actual depth of a swimming pool based on perceived depth, given a refractive index of water at 1.33. The observer's eye level is 1.8 meters above the edge of the pool, and the pool width is 12 meters. The perceived depth is estimated at 2.4 meters. The critical angle calculated using Snell's Law is approximately 48.57 degrees, but the participants note that the small angle approximation is not applicable in this scenario. The challenge lies in determining the actual depth without direct angle measurements.

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  • Understanding of Snell's Law and refraction
  • Knowledge of critical angles in optics
  • Familiarity with the concept of perceived vs. actual depth
  • Basic trigonometry related to angles and triangles
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  • Research the effects of refractive index on visual perception
  • Explore the concept of critical angles in different mediums
  • Learn about the limitations of small angle approximations in optics
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Homework Statement



a man stands by a swimming pool that is completley filled with water. his eyes are 1.8 meters directly above the edge and the pool is 12 meters wide.
when he looks toward the corner on the opposite side of the pool , he estimates the pool to be 2.4 meters deep. if the refractive index of water is 1.33 calculate the actual depth of the pool.

Homework Equations



no equations given, but just a statement "the small angle approxmitaion sin theta = tan theta = theta is not appropriate for this situation."

The Attempt at a Solution



i tried using snells law but i get no where as no angles are given and i can't use the small angle approximation . the most i can work out is the critical angle which is sin^-1 (1/1.33) that gives 48.574 deg. but i don't think its going to help much?
im very stuck
 
Last edited:
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Relevant equations?
Attempt at a solution?

To start answer the question: How do we perceive depth?
 

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