In Young's double slit experiment, the distance between the two coherent sources is ' d ' and the distance between the source and screen is ' D '. When the wavelength ( ) of light source used is d^2 3 D , then n^ th dark fringe is observed on the screen, exactly in front of one of the slits. The value of ' n ' is

Step-by-step solution

aligned S ₂ P & = ( D ^2+ d ^2 )^ 1 / 2 & = D [1+ d ^2 D ^2 ]^ 1 / 2 aligned Using binomial equation, aligned & S ₂ P = D [1+ 1 2 ~d ^2 D ^2 ]^ 1 / 2 = D + d ^2 2 D & Path difference = d ^2 2 D aligned For dark fringe, d ^2 2 D =(2 n -1) 2 aligned & d ^2 2 D =(2 n -1) d ^2 6 D & 2 n -1=3 & n=2 aligned