Actual vs percieved depth. optics question

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The discussion revolves around calculating the actual depth of a swimming pool based on perceived depth, considering the refractive index of water. The individual estimates the pool's depth at 2.4 meters while standing 1.8 meters above the edge. They attempted to apply Snell's Law but faced challenges due to the lack of angle measurements and the inapplicability of the small angle approximation. The critical angle was calculated as approximately 48.57 degrees, but its relevance to solving the problem is questioned. The conversation highlights the complexities of visual perception and optical principles in determining actual versus perceived depth.
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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
 
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Relevant equations?
Attempt at a solution?

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

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