In each of the cases below a plane EM wave propagates in a homogeneous medium, satisfying:...

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In each of the cases below a plane EM wave propagates in a homogeneous medium, satisfying: case I: Ex = E cos(kz - wt), case II: Ex = -E0 cos(kz + wt), case III: Ex = 2E0 cos(kz - wt + /2), Ey Eo cos(kz - wt); = Ey=2Eo cos(kz+wt+/2); Ey=2E0 cos(kz - wt); where En, k, w are constants, and E = 0 in all three cases. (a) In each of the above three cases, determine the polarization state of the wave by tracing out the tip of its vector at a fixed z (for simplicity take z=0). Specify in each case if the wave is linearly, circularly (left or right-handed) or elliptically (left or right-handed) polarized with respect to the receiver. (b) The wave from case I of intensity Io is incident on a set of two perfect polarizers, each located in a plane perpendicular to the z-axis. The first polarizer along the direction of propagation has its polarization axis at an angle /3 away from the y-axis and at an angle 7/6 away from the x-axis. The second polarizer has its polarization axis at an angle 7/6 away from the y-axis and at an angle /3 away from the x-axis. Determine the intensity of the wave after it passes through both polarizers. In each of the cases below a plane EM wave propagates in a homogeneous medium, satisfying: case I: Ex = E cos(kz - wt), case II: Ex = -E0 cos(kz + wt), case III: Ex = 2E0 cos(kz - wt + /2), Ey Eo cos(kz - wt); = Ey=2Eo cos(kz+wt+/2); Ey=2E0 cos(kz - wt); where En, k, w are constants, and E = 0 in all three cases. (a) In each of the above three cases, determine the polarization state of the wave by tracing out the tip of its vector at a fixed z (for simplicity take z=0). Specify in each case if the wave is linearly, circularly (left or right-handed) or elliptically (left or right-handed) polarized with respect to the receiver. (b) The wave from case I of intensity Io is incident on a set of two perfect polarizers, each located in a plane perpendicular to the z-axis. The first polarizer along the direction of propagation has its polarization axis at an angle /3 away from the y-axis and at an angle 7/6 away from the x-axis. The second polarizer has its polarization axis at an angle 7/6 away from the y-axis and at an angle /3 away from the x-axis. Determine the intensity of the wave after it passes through both polarizers.