Question

i) Sketch a ray diagram of a normally polarized electromagnetic field interacting with a glass/air interface. Calculate the critical angle for the glass/air interface (nI(pure glass).5; n2(air)-l). For this calculation, you can ignore the polarization because the critical angle is the same for either normal or parallel normalisation. ii)Derive an expression for the wavelength of the transmitted wave as a function of the refractive index ni at®i-0c from the phase matching boundary requirement at the glass/air interface (see Fig. 1). Calculate a numerical value for the speed of propagation (phase speed) of the wave in air. Comment on its value. iii) Repeat ex.(ii) for a value a-t/3, larger than iv) Show, from Maxwell's equations, that the speed ) of a plane wave in a medium of refractive index n is given by - Considering the result obtained in (iv) and the numerical value obtained in (iii), it seems to demonstrate that the transmitted wave amplitude is zero, or no transmitted wave exists. However, the boundary conditions on E and H require the existence of.a transmitted wave; show that this is the case. v)

Answer 1

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