In Young’s double slit experiment, light of wavelength $ 5000\, \text{Å} $ is used. The slit separation is $ 3\, \text{mm} $, and the screen is $ 20\, \text{cm} $ away. If a $ 1\, \text{mm} $ transparent plate is introduced in front of one slit, and the fringe pattern shifts by $ 6\, \text{mm} $, then the refractive index of the plate is: