 Full-cycle phase-plate invisibility

In a monochromatic two-path interferometer, an ideal phase plate of thickness $t$ and refractive index $n$ adds phase $2\pi (n-1)t/\lambda$ at normal incidence. The interference pattern is unchanged when $(n-1)t=m\lambda$ for integer $m$, provided transmitted amplitudes and alignment are unchanged. Calling the smallest index requires specifying the admissible range; $n>1$ excludes the optically null $n=1$ solution.