Solve Refraction Problem: Archimedes' Gold Crown

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SUMMARY

The discussion revolves around solving a refraction problem related to Archimedes' gold crown using Snell's Law. The refractive index of the dirty bath water is given as 1.35, and the angle of incidence is calculated to be 37.37°. The challenge lies in determining the depth of the water in the bathtub, which is one meter high, while considering the apparent location of the crown observed at a 35° angle above the water's edge. A diagram is suggested as a necessary tool for visualizing the problem.

PREREQUISITES
  • Understanding of Snell's Law (n1 sin θ1 = n2 sin θ2)
  • Basic knowledge of angles and trigonometry
  • Familiarity with the concept of refractive index
  • Ability to interpret geometric diagrams
NEXT STEPS
  • Study the application of Snell's Law in various refraction scenarios
  • Learn how to create and interpret diagrams for optical problems
  • Explore the relationship between angles of incidence and refraction
  • Investigate the effects of different refractive indices on light behavior
USEFUL FOR

Students studying physics, particularly those focusing on optics and refraction, as well as educators looking for practical examples of Snell's Law applications.

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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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