(i) Derive the Fresnel reflection coefficients for TE and TM plane waves for the single interface problem. (ii) Explain how Snell's law follows from the phase matching condition. (iii) Find the condition for total internal reflection, and explain why the wave is evanescent on one side of the interface. Under what condition can total internal reflection occur, and in which medium is the wave evanescent? (iv) For the lossless medium case, what happens to the amplitude of the reflection coefficient when total internal reflection occurs? (v) Using the complex Poynting's theorem, show that the evanescent wave can only carry reactive power in a lossless medium