The relationship between the index of refraction and the change in the direction angle of the a ray as it goes across a medium is given by Snell's law: \(n_{1}\sin\theta _{1}=n_{2}\sin\theta _{2}\) wh...The relationship between the index of refraction and the change in the direction angle of the a ray as it goes across a medium is given by Snell's law: \(n_{1}\sin\theta _{1}=n_{2}\sin\theta _{2}\) where \(n_{1}\) and \(\theta _{1}\) are values measured on side of the boundary and the subscript 2 is for the material on the other side of the boundary.