Evacuated-cell interferometric refractometry ($n-1=N{\lambda }_0/l$)

Evacuating a transparent cell of optical length $l$ in one coherent beam changes its optical path by $l(n-1)$ relative to an unchanged cell in the other beam. With vacuum wavelength ${\lambda }_0$, the number of completed fringe periods is $N=l(n-1)/{\lambda }_0$. The initial maximum is not an additional completed period. Counting only integer fringes leaves a phase uncertainty of order one fringe unless the final fractional phase is measured; the corresponding index scale is ${\lambda }_0/l$. Fixed equal window contributions cancel in the path difference.