Snell's law of refraction at the interface between 2 isotropic media is given by the equation: n_1 * sin(theta_1) = n_2 * sin(theta_2), whereθ_1 is the angle of incidence andθ_2 is the angle of refraction. n_1 is the refractive index of the optical medium in front of the interface and n_2 is the refractive index of the optical medium behind the interface. How can this be expressed in vector form: n_1(bfi * bfn) = n_2(bft * bfn), where bfi(i_x, i_y, i_z) and bft(t_x, t_y, t_z) are the unit directional vectors of the incident and transmitted rays respectively. bfn(n_x, n_y, n_z) is the unit normal vector to the interface between the two media pointing from medium 1 with refractive index n_1 into medium 2 with refractive index n_2. Further, how can the Snell's law of refraction be expressed in the following way: t = mu * bfi + bfn * sqrt(1 - mu² * (1 - (ni)²)) - mu * bfn * (ni), where mu = n_1/n_2 and bfn * bfi = n_x * i_x + n_y * i_y + n_z * i_z denotes the dot (scalar) product of vectors bfn and bfi.