Snell's Law is an equation from optics which describes how a light ray behaves when it passes from one medium to another with different indices of refraction. It says that n1sin(⊖1) = n2sin(⊖2) where n1 and n2 are the indices of reffraction and ⊖1 and ⊖2 are the angles of incidence. Suppose that you measure n1=1.4, n2=0.9, and ⊖1=pi/6 a) simplify the equation using the values provided and convert it to a root-finding problem for ⊖2. (A root-finding problem is a problem in which f(x)=0 and the goal is to find x) B) Use the Intermediate Value Theorem to show that a solution exists for ⊖2 between 0 and pi/2. Clearly show that the conditions of the theorem are met, and state the appropriate conclusion.
Snell's Law is an equation from optics which describes how a light ray behaves when it passes from one medium to another with different indices of refraction. It says that n1sin(⊖1) = n2sin(⊖2) where n1 and n2 are the indices of reffraction and ⊖1 and ⊖2 are the angles of incidence. Suppose that you measure n1=1.4, n2=0.9, and ⊖1=pi/6
a) simplify the equation using the values provided and convert it to a root-finding problem for ⊖2. (A root-finding problem is a problem in which f(x)=0 and the goal is to find x)
B) Use the Intermediate Value Theorem to show that a solution exists for ⊖2 between 0 and pi/2. Clearly show that the conditions of the theorem are met, and state the appropriate conclusion.
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