= Solution
Treat the transparent plate as a <phase plate> at normal incidence. Its extra optical path is $(n-1)50\lambda$. An unchanged <interference> pattern requires an integer number of full <phase> cycles:
$$
50(n-1)=m\in\mathbb Z,\qquad n=1+\frac m{50}.
$$
For <full-cycle phase-plate invisibility> in an ordinary nontrivial material with $n>1$, the two smallest are \b[$n=1.02$ and $1.04$]. If the optically null case $n=1$ is admitted, the first two nondecreasing-$n\ge1$ values are $1$ and $1.02$. A different allowed range of <refractive indices> would need to be specified before calling these the absolute smallest possibilities.
Back to article page
