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

[aliciadombros]

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?

 

[kuruman]

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?

 

[aliciadombros]

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?

 

[kuruman]

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.

 

[aliciadombros]

Thank you for the help. I looked in the back of the book and it said 35 degrees, but I guess it's wrong.