A half-wave plate has a phase retardation of G = p. Assume that the plane is oriented so that the azimuth angle (i.e., the angle between the x-axis and the slow axis of the plate) is y. (a) Find the polarization state of the transmitted beam, assuming that the incident beam is linearly polarized in the y direction. (b) Show that a half-wave plate will convert right-hand circularly polarized light into left-hand circularly polarized light, and vice-versa, regardless of the azimuth angle of the plate. (c) E7 is a nematic liquid crystal with no = 1.52 and ne = 1.75 at l = 577 nm. Find the half-wave-plate thickness at this wavelength, assuming that the plate is made in such a way that the surfaces are parallel to the directors (i.e. a plate).