Several recent radio astronomical observations (primarily interferometer visibility measurements) have yielded values of α, the power-law index of the interstellar density power spectrum. An examination of these observational results shows that the inferred value of α depends on the angular separation of the antennas making the measurement. For antenna separations greater than a few thousand kilometers, the value of α is equivalent to the "Kolmogorov" value of 3.67. For baselines of a few hundred kilometers or less, the inferred α approaches 4.0. We point out that these observations are as expected if the interstellar density spectrum is Kolmogorov, with an inner scale of 50-200 km. Such a scale is comparable to plasma microscales (such as the ion Larmor radius or the ion inertial length) for either the warm ionized component of the McKee-Ostriker model of the interstellar medium, or the extended envelopes of prominent H regions reported by Lockman and Anantharamaiah. The observed inner scale is considerably smaller than plasma microscales in the hot intercloud phase of the interstellar medium. We conclude that the host plasma for the irregularities responsible for interstellar scintillation is either the McKee-Ostriker warm ionized component, the envelopes of H II regions, or some ionized medium with similar physical characteristics.