A wave-plate was constructed by etching a sub-wavelength grating into GaN (n=2.4), giving 50% GaN and 50% air. Using the effective medium approximation for parallel plates (L_x=0 and L_y=1) in the latest notes, estimate the birefringencen. A suspicious "quarter-wave" plate is checked by placing it between parallel polarizers (e.g. both horizontal): the transmitted intensity when the plate is oriented @ 45 degrees to the polarizers is 70% compared to the aligned position. Starting from the Mueller matrix for a rotated retarder, estimate the actual retardation in degrees.