Why Does Snell's Law Give Incorrect Results When Using Certain Formulas?

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Gajan1234
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At the start of the chapter the book told me to use this formula to find refractive index: N= Sin(i)/Sin(r)
How ever later in the section they showed me to use this formula when three quantities are given : NxSin(i)=NxSin(r)
I tried apply the same method to a question, it gave me a wrong answer. Why is it?
 

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Your second equation is not correct. You must understand what the symbols mean. What is i? What is r? What is Nx? Then the relation between the two equations you wrote will become clear.
 
Snell's law should be n1sinθ1 = n2sinθ2, where n1 is the index of refraction of the incident medium with θ1 being the angle of incidence, along with n2 as the index of refraction of the refractive medium with its angle of refraction being θ2. The three quantities you are asking about are used to find a last unknown variable, by algebraically placing the 3 known variables on one side of the = sign and solving for the other side, the unknown variable.