Solve Refraction Problem: Archimedes' Gold Crown

  • Thread starter Thread starter thenabforlife
  • Start date Start date
  • Tags Tags
    Refraction
Click For 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.
thenabforlife
Messages
2
Reaction score
0

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.
 
Physics news on Phys.org
We really need a diagram to begin with!
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Solve Archimedes Problem: Find Crown's Density
  • · Replies 4 ·
Replies
4
Views
2K
How much gold did the goldsmith steal from King Hero's crown?
  • · Replies 1 ·
Replies
1
Views
3K
Archimedes' Principle-Gold Crown problem
  • · Replies 4 ·
Replies
4
Views
18K
Deriving Equation Relating Angle of Incidence to the Angle of Refracti
  • · Replies 6 ·
Replies
6
Views
2K
Light refraction problem in water & air
  • · Replies 4 ·
Replies
4
Views
8K
Optics, involving index of refraction
  • · Replies 4 ·
Replies
4
Views
2K
Find magnification of a fish in a fish bowl
  • · Replies 1 ·
Replies
1
Views
5K
Is Snell's Law Misleading in Refraction Calculations?
  • · Replies 4 ·
Replies
4
Views
8K
Solving Snell's Law: Find Incident & Refractive Angles
  • · Replies 12 ·
Replies
12
Views
4K
Speed of a moving laser due to refraction
  • · Replies 6 ·
Replies
6
Views
2K