The real and imaginary refractive indices of water ice in the far infrared (IR) are used in the satellite interpretation of cloud properties as well as to obtain information on ice throughout the solar system. However, few measurements of these values exist. We have measured the real and imaginary refractive indices of water ice in the far IR every 10 deg over the temperature range of 106-176 K. Ice films ranging from 0 to 140 microm thick were grown by the condensation of water vapor onto a cold silicon substrate, and the film transmission was measured from 650 to 50 cm(-1). The thickness of the ice films was determined using optical interference from a reflected He-Ne laser (lambda = 623.8 nm). The optical constants were then determined by simultaneously fitting the calculated spectra of films of varying thickness to their respective measured transmission spectra with an iterative Kramers-Kronig technique. The results are compared with previously measured data and show large discrepancies at some wavelengths while good agreement exists at others. Possible reasons for the differences are discussed. Our data clearly distinguish crystalline and amorphous ice. In addition, we note a slight shoulder in our spectra, which can be used to distinguish between cubic and hexagonal ice, although this distinction is difficult.