Answer Happy

C sti C.2 Electromagnetism (F a) Unpolarized light of wavelength 500 nm is normally incident upon a slab of calcite whose optic axis is aligned perpendicular to the incident ray direction, as illustrated below. Optic axis Lic t the illustration. 15 The incident light excites oscillating dipoles on the front surface of the cal- cite. Two distinct Huygens secondary wavelets are found to propagate away from each induced dipole, as shown in i) Copy the two wavelets and indicate on your sketch the direction of their fields at various points on the wavefronts. (You should explain your reasoning.) Calcite has a birefringence of magnitude Anl=0.17 at 500 nm. ii) Indicate the fast and slow axes on your sketch. iii) Calculate the minimum thickness of a calcite half wave plate for 500 nm light. b) The left and right circular polarization states can be represented 2 12 R 1 (9) in the ry Cartesian system. c=ta ) Using the CR circular basis , the Jones matrix of a “circular wave-plate" has the =(expl (exp(-18/2) exp(18/2) (2) , where 8 = 8e - de is the retardation of the R state relative to the state. (i) Find J, the Jones matrix of the circular wave-plate in the Cartesian ry frame. (ii) Hence state how the circular waveplate would affect a linearly polarized light 17 wave. [2] (iii) Explain your answer to part (ii) by considering the incident linearly polarised wave to be a superposition of Land R states. [2]