Group refractive index calculation by difference approximation for length measurement

In this study, the possibility of employing a difference approximation to facilitate calculation of the group refractive index of air (GRA) was investigated. The forward, backward, and central difference methods were used to numerically approximate the first-order derivatives of the phase refractive index based on the Edlén empirical equations. To confirm the validity of the calculations, the calculated results were compared with the theoretical analysis results and the values in a related paper. It was found that the GRA computation could be easily approximated by the two-point central difference method with a step size of 10 nm.