How to Calculate d(theta0)/d(theta1) in Snell's Law?

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To calculate d(theta0)/d(theta1) in Snell's Law, start with the relationship v0/v1 = R, leading to R sin(theta1) = sin(theta0). Taking the derivative of both sides with respect to theta1 reveals that theta0 is a function of theta1, suggesting the use of the chain rule. This approach allows for the derivation of the relationship between the angles. The discussion emphasizes the importance of applying geometric and analytical methods to solve the problem effectively.
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I have light incident from plane with velocity v0 into plane with velocity v1. Obviously, according to Snell's law, v0/v1=sin(theta0)/sin(theta1), where theta0 and theta1 are the angles with regard to the vertical line. How to calculate d(theta0)/d(theta1)? There are probably arguments from geometry and analysis.
Thanks a lot!
 
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First, for simplicity write v0/v1 = R. Then

R sin θ1 = sin θ0

Now take the derivative of each side with respect to θ1. On the right-hand side, θ0 is a function of θ1. What rule does that suggest?
 
Thanks a lot! That was clear!
 
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