Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / B7 / d / 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:For full-cycle phase-plate invisibility in an ordinary nontrivial material with $n>1$, the two smallest are $n=1.02$ and $1.04$. If the optically null case $n=1$ is admitted, the first two nondecreasing-$n\ge 1$ 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.