4. (a) Show that light that is linearly polarized in the x direction can be decomposed into two circularly polarized components: E, = 1Excos kz -of ) - psin kz - of) and E. =1E &cos(kz - cf) + psin( kz - of). (b) The linearly polarized light in (a) is incident at z = 0 on an optically active material, for which the propagation constants for left- and right-circularly polarized light are k, and , After travelling a distance d through the material, kid= kid + x . Show that the light is now linearly polarized in the y direction. (c) Show that the angle of rotation of the linear polarization is given by B = where 2 is the free-space wavelength, m, and m, are the refractive indices for left- and right-circularly polarized light, and d is the physical thickness of the material