On placing a thin film of mica of thickness 12 10⁻⁵ ~cm in the path of one of the interfering waves in Young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to width of a bright fringe. If wavelength used is =6 10⁻⁵ ~cm , the refractive index of mica is

Step-by-step solution

Path difference due to the mica film: ( -1) t The shift in the pattern be yand the corresponding path difference can be written as: x= y D d =( -1) t y= d D ( -1) t Fringe width is = D d , so, y= ( -1) t If the shift is equal to the fringe width aligned & = ( -1) t & ( -1) t= & = t +1= ( 6 10⁻⁵ 12 10⁻⁵ )+1=1.5 aligned