Answer Happy

a) An electromagnetic plane wave travelling through free space in the z direction has components of E and B which each have the general form f(kz - wt). [2] (i) Use Gauss's Law to show that E is transverse. (ii) For the case E = Eoe sin(kz - wt) use the Maxwell-Faraday equation to find B, and hence show that B is also transverse, perpendicular to E and with magnitude B = E/c. Find the Poynting vector and the intensity of the wave. [3] [3] 1 b) The right circular polarisation state can be represented by R = - (-4) in an xy Cartesian system. Find R', the Jones vector of this state expressed in the r'y' frame which is rotated anti-clockwise from ry by angle, as illustrated below left. You should express your answers in terms of R. [3] [Hint: You will find it useful to recall that the matrix R(0) converts a vector whose components are expressed in the x'y' frame to the ry representation.] Polariser Unpolarised R(0) = cos sin 6 sin 0 -5640) cos Quarter-wave plate y y' Ꮎ Ꮎ X