Describe Young's double slit experiment to produce interference pattern due to a monochromatic source of light. Deduce the expression for the fringe width.

Conditions for Young’s double slit experiment are:

(i) The sources should be monochromatic and originating from common single source.

(ii) The amplitudes of the waves should be equal.

Let S₁ and S₂ be two coherent sources separated by a distance d.

Let the distance of the screen from the coherent sources be D. Let point M be the foot of the perpendicular drawn from O, which is the midpoint of S₁ and S₂ on the screen. Obviously point M is equidistant from S₁ and S₂. Therefore the path difference between the two waves at point M is zero. Thus the point M has the maximum intensity.

Now, Consider a point P on the screen at a distance y from M. Draw S₁N perpendicular from S₁ on S₂ P. 


The path difference between two waves reaching at P from S₁ and S₂ is given by, 

 

Since, D >> d, 

Expression for Fringe Width:

Distance between any two consecutive bright fringes or any two consecutive dark fringes are called the fringe width. It is denoted by . 
Let,  be the distance of two consecutive fringes. Then, we have



So, fringe width is 
Fringe width is same for both bright and dark fringe.