In Young's double slit experiment, the two slits are d distance apart. Interference pattern is observed on the screen at a distance D from the slits. Fist dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of the light is.

Step-by-step solution

Consider the following diagram: The dark fringe is produced at a point just opposite to the slit S₁ , i.e., y₁= d 2 For dark fringe, path difference is odd multiple of half of the wavelength: x=(2 n-1) 2 From the figure, relation between fringe location and path difference can be obtained as: aligned & = y D = x d & y= x D a =(2 n-1) ( 2 ) ( D a )=(2 n-1) D 2 d aligned where n=1,2,3, aligned & d 2 =(2 n-1) D 2 d & = d^2 (2 n-1) D aligned For n=1 , = d^2 D