Young’s double-slit experiment — UPSC IFoS 2020 Physics PYQ

A glass chamber 25\text{ mm} long filled with air is positioned in front of one of the secondary sources in Young's experiment. The air is removed from the chamber and a test gas is entered in its stead. On comparing the fringe system corresponding to air with that of the test gas, it is found that the entire interference pattern on the screen was displaced by 21 bright bands towards gas-containing chamber. Given that \lambda = 656{\cdot}2816\text{ nm} for which the refractive index of air is n_a = 1{\cdot}000276. Determine the refractive index of the gas (n_g).