A critical angle method was used to measure the index of refraction of a solid medium when an air gap between the prism and the medium is present. The gap effect was analyzed both numerically and experimentally. Since the total internal reflection is severely disturbed by the large gap, determination of the critical angle and the resulting refractive index becomes ambiguous and inaccurate. By using an index matching fluid, we could determine the index of refraction with an uncertainty of ${pm}2{ imes}1^{-3}$ even when the gap is as large as 1 ${mu}m$.