What is the angle of incidence on a cubic zirconia crystal submerged in oil?

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SUMMARY

The discussion centers on calculating the angle of incidence for a light ray entering a cubic zirconia crystal submerged in oil. The correct application of Snell's Law, represented as n1 sin(θ1) = n2 sin(θ2), reveals that the angle of incidence (θ1) is 39 degrees when using the correct indices of refraction: 1.46 for oil and 2.18 for cubic zirconia. The confusion arose from an incorrect assumption regarding the indices of refraction, leading to an erroneous conclusion of 35 degrees. Ultimately, the consensus confirms that the accurate angle of incidence is indeed 39 degrees.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Knowledge of indices of refraction for different materials
  • Familiarity with angle measurement in degrees
  • Basic principles of light refraction
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  • Research the indices of refraction for various materials, including cubic zirconia and oil
  • Study the derivation and applications of Snell's Law in optical physics
  • Explore common errors in optical calculations and how to avoid them
  • Learn about the practical applications of cubic zirconia in jewelry and optics
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This discussion is beneficial for physics students, optical engineers, and anyone involved in materials science or jewelry design who seeks to understand light behavior in different mediums.

aliciadombros
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A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray enters one face of the zirconia crystal, then travels at an angle of 25 degrees with respect to the normal. What was the ray's angle of incidence on the crystal?



Relevant equations:

n1 sin(θ1) = n2 sin(θ2)



n1 sin(θ1) = n2 sin(θ2)
2.18 sin(θ1) = 1.46 sin(65)
θ1=37 degrees but the real answer is 35.

Any help to where I went wrong?
 
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Hi aliciadombros and welcome to PF. What is medium 1 and what is medium 2? It seems that if you are looking for the angle on the crystal and the unknown angle is θ1, then medium 1 must be oil and medium 2 must be zirconia. You used 2.18 for n1. Is the index of refraction for oil 2.18?
 
I must've flipped them around. The index of refraction for oil is 1.46. But, when I plugged the information into the equation the way you told me,

n1 sin(θ1) = n2 sin(θ2)
1.46 sin(θ1) = 2.18 (sin 25)
θ1= 39, not 35.

Am I using the wrong angle measurement or is it my calculations that are off?
 
Your last solution is correct. I plugged in the numbers and the answer that I get agrees with yours, 39 degrees. How sure are you that the answer is 35 degrees? Sometimes posted answers or answers in the back of the book are incorrect.
 
Thank you for the help. I looked in the back of the book and it said 35 degrees, but I guess it's wrong.
 

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