We investigate experimentally the lifetime of the photons in a cavity containing a medium exhibiting strong positive dispersion. This intracavity positive dispersion is provided by a metastable helium gas at room temperature in the electromagnetically induced transparency regime, in which light propagates at a group velocity of the order of 10⁴ m·s⁻¹. The results definitely prove that the lifetime of the cavity photons is governed by the group velocity of light in the cavity and not its phase velocity.