Uncertainty in length conversion due to change of sensitivity coefficients of refractive index

Abstract

A value of length measured in air should be converted to the value in vacuum for the purpose of comparison. The typical values of the sensitivity coefficients for a particular wavelength (e.g. 632.99nm) under standard environmental conditions are widely available. Because all measurements are not performed under standard environmental conditions and the sensitivity coefficient is affected by atmospheric pressure, temperature, and humidity, one question arises naturally: how does a measurement change with environmental conditions? This study investigates the uncertainty in length conversion due to the change of sensitivity coefficients of refractive index. We also clarify that there is no significant difference in conversion uncertainties via sensitivity coefficients of phase and group refractive indexes.