Solve Refraction Problem: Archimedes' Gold Crown

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AI Thread Summary
The discussion revolves around solving a physics problem related to Archimedes' gold crown and light refraction in water. The problem involves determining the depth of the water in a bathtub where the crown is submerged, given the refractive index of the water and the angle of incidence. Participants highlight the need to apply Snell's Law and suggest that a diagram would aid in visualizing the situation. The main challenge lies in incorporating the apparent location of the crown and the bathtub's height into the calculations. Clarifying these elements is essential for reaching a solution.
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Homework Statement



Archimedes left his gold crown lying on the bottom of his partially filled bathtub. Although he did not know Snell's Law in fact he thought it was Smell's Law (they don't bathe very often back then), or even that the refractive index of dirty bath water was 1.35, he did note that light appeared to bend as it entered the water. As he peers into the water at 35° above the water's edge he sees the crown one meter away from the edge of the tub. His tub is one meter high. Given the information provided, determine the depth on the King's bath water.


Homework Equations



Snell's law- n1 sin θ1= n2 sin θ2


The Attempt at a Solution



I found the angle of incidence which was 37.37 but I don't know how to incorporate the apparent location of the crown and the height of the bathtub into this problem. Plz help. ty.
 
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We really need a diagram to begin with!
 
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