Error Propagation Snell Law
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Fractional Uncertainty
Analysis in snell's Law? I am having trouble coming up with the correct formula to account for uncertainty in a snell's law problem. It gives me θ1 = 22.03 +/- .2 and θ2 = 14.45 +/- .2 and n1 = 1.0000. It asks me to find n2 and its uncertainty from the data given. I know how to get n2, that is the easy part. The difficulty snell's law is how... show more I am having trouble coming up with the correct formula to account for uncertainty in a snell's law problem. It gives me θ1 = 22.03 +/- .2 and θ2 = 14.45 +/- .2 and n1 = 1.0000. It asks me to find n2 and its uncertainty from the data given. I know how to get n2, that is the easy part. The difficulty is how do I derive a formula to account for the uncertainty? 1 following 1 answer 1 Report Abuse Are you sure you want to delete this answer? Yes No Sorry, something has gone wrong. Trending Now Erykah Badu Tom Cruise Samsung Note7s Adrien Broner Faith Hill Car Insurance Kylie Jenner Contact Lenses Great Lakes Personal Loans Answers Best Answer: The general formula for finding the uncertainty of error propagation is: Let f be a function of the variables x1,x2,...,xn with uncertainties σ1, σ2,... σn. Then the uncertainty of f is given by: σ_f = √ [ (∂f/∂x1)² ·(σ1)² + (∂f/∂x2)² ·(σ2)² + ... + (∂f/∂xn)² ·(σn)² ] For n2 = n1·sin(θ1)/sin(θ2) σ_n2 = √[ (∂n2/∂θ1)² ·(σ_θ1)² + (∂f/∂θ2)² ·(σ_θ2)²] The partial derivatives are ∂n2/∂θ1= ∂(n1·sin(θ1)/sin(θ2)) /∂θ1 = (n1/sin(θ2)) ·
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