Precision spectroscopy on molecular tellurium is performed by measurin
g the frequency difference between the observed lines and an eigenfreq
uency of a high-finesse cavity mode. The mode frequency is derived fro
m a measurement of the cavity's free spectral range taking into accoun
t the cavity dispersion due to phase shifts in the dielectric mirror c
oatings. The experimental technique is based on dual frequency modulat
ion and is applied to determine the transition wavenumbers of several
lines in Te-130(2) near 467 nm with an uncertainty of 2 x 10(-8).