The far ir reflectivity of a pure single crystal of KI at liquid helium, liquid nitrogen, and room temperature has been measured from 10 μ to 700 μ. Kramers-Kronig analysis, and a two-oscillators Lorentz analysis lead to close results concerning the refractive index n, and the absorption index k in the whole ir spectrum, with maximum values of n and k ranging from 4 to 8. The strongest Lorentz oscillator has a frequency at 80°K (ν1 = 110 cm−1) close to the transverse optic frequency recently determined from neutron scattering at 95°K (TO = 107 ± 1.3 cm−1). The strength of the second Lorentz oscillator decreases rapidly when the temperature is lowered. Its frequency (ν2 = 150 cm−1 at 80°K) is such that it can be considered as the TO + TA combination at point L of the first Brillouin zone, which is ir active, and expected at 152.7 ± 3 cm−1 from neutron scattering. Absorption bands, localized in the gap determined by neutron scattering as extending from 104–143 μ (96–70 cm−1), are induced by sodium, cesium, and chlorine ions impurities. A peak of absorption in the acoustic phonons spectrum is induced by sodium ion impurities at 63 cm−1 close to a maximum in the frequency distribution function for the normal modes of vibration of KI computed recently by Cowley et al. Bromine ions, on the other hand, lead to a general background absorption.