Total Internal Reflection (TIR) is the phenomenon whereby a light wave incident on a boundary is completely reflected when the wave’s incidence angle exceeds a critical angle, θc . For decades there has been debate about whether amplified TIR from a medium exhibiting optical gain is possible, and desire for a theory to explain it. Authors have suggested theories both in favor and in doubt of the phenomenon’s existence, and experimental evidence has arose supporting the existence and seemingly simultaneously contradicting proposed theoretical models. In this thesis, reflection coefficients for plane waves are calculated by satisfying boundary conditions from Maxwell’s equations at the reflecting surface for both optically lossy and gainy media. Plane wave reflectivity is found to exhibit a discontinuous jump from below unity to above as the incidence angle passes through the critical angle, confirming the existence of amplified TIR. Fourier analysis is used to show that finite beams also exhibit amplified TIR, but do not experience the surprising discontinuous jump in reflectivity at the critical angle.