Mie theory computations of the refraction efficiency for spherical particles are compared with predictions of the Rayleigh, Rayleigh-Gans and Anomalous Diffraction approximations. Attention is given to the intermediate region of particle size, where for extinction the Rayleigh-Gans and Anomalous Diffraction approximations have been shown to merge with each other and with Mie computations. In this region the Mie refraction efficiency is shown to have a first maximum which is not given by any approximation. The Rayleigh and Rayleigh-Gans refraction efficiencies are independent of particle size and approximate to the Mie results in the intermediate region, but not at larger particle sizes. Apart from the first maximum, the AD approximation is shown to closely predict the extrema and zeros of the refraction efficiency. In the intermediate region the Mie computations reveal a first maximum in the refraction efficiency which is not modelled by either of the RG or the AD approximations. Consequently a region where the Rayleigh-Gans and Anomalous Diffraction approximations merge with each other and with Mie computations is not found for refraction. The first maximum in refraction efficiency predicted by the Mie theory occurs when the optical wavelength inside a particle is about 20% greater than the particle's diameter. It is shown to result mainly from the contributions to refraction by the magnetic dipole and electric quadrupole.