Utilizing a new average atom code, we calculate the index of refraction in C, Al, Ti, and Pd plasmas and show many conditions over which the bound-electron contribution dominates the free electrons as we explore photon energies from the optical to 100 eV (12 nm) soft x rays. For decades measurement of the electron density in plasmas by interferometers has relied on the approximation that the index of refraction in a plasma is due solely to the free electrons and therefore is less than 1. Recent measurements of Al plasmas using x-ray laser interferometers observed fringes bending in the opposite direction than expected due to the bound-electron contribution causing the index of refraction to be larger than 1. During the next decade x-ray free-electron lasers and other sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths, so understanding the index of refraction in plasmas is essential.