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

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SUMMARY

The discussion focuses on calculating the derivative d(theta0)/d(theta1) in the context of Snell's Law, which describes the relationship between the angles of incidence and refraction of light as it passes through different media. The equation v0/v1 = sin(theta0)/sin(theta1) is established, where v0 and v1 are the velocities of light in two different media. The user suggests simplifying the ratio to R = v0/v1 and derives the relationship R sin(theta1) = sin(theta0). The next step involves taking the derivative of both sides with respect to theta1, indicating that theta0 is a function of theta1, which leads to the application of the chain rule in calculus.

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ytht100
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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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