A dextrose solution is optically active and is characterized by a polarization vector (electric dipole moment per unit volume): P = γ Ñx E, where γ is a real constant which depends on the dextrose concentration. The solution is non-conducting and nonmagnetic. Consider a plane electromagnetic wave of (real) angular frequency ω propagating in such a solution. For definiteness, assume that the wave propagates in the +z direction. Also assume that !" # ≪ 1 (a) Find the two possible indices of refraction for such a wave. For each possible index, find the corresponding electric field. (b) Suppose that linearly polarized light is incident on the dextrose solution. After traveling a distance L through the solution, the light is still linearly polarized, but the direction of its polarization has been rotated by an angle φ (called Faraday rotation). Find φ in terms of L, γ, and ω.