In a semiconductor microcavity, excitons (bound electron-hole pairs) and cavity photons couple with Rabi frequency Ω_R. The coupled modes form lower (LP) and upper (UP) polariton branches. LP has a Mexican-hat dispersion minimum — polaritons relax there and, above a threshold pump rate, undergo Bose-Einstein condensation. Being half-light, polariton BEC occurs at room temperature in some materials. Hopfield coefficients |X|² (exciton fraction) and |C|² (photon fraction) give the mixing.