Youngs Double slit experiment

 Young Double slit experiment

Mathematical Approach of Youngs double slit experiment

Let two light source S1 and S2 are narrow parallel slit sepearated by a distance 'd'  emitted from Source S. The wave from Both slit behave as it is emerging from S1 and S2.They travel in same medium and reaches at screen which is situated at a distance of D from slit source.

Let Point O is at equidistance from point S1 and S2 in same phase .Hence the point O will be Bright called as central bright. Now let R be any point at a distance 'x' from O . the path difference  between  the waves reaching R from  S1 and S2 is (S1R - S2R) . Thus from figure above, Triangle S1MR and Triangle S2NR is right angled triangle.

Applying phythagoras theorem in S1MR ,

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Fringe width

The distance between the center of two adjacent bright or dark bands is called as fringe width.

Fringe width of bright Bands: Let us consider two adjacent bright frindge at a distance xn  and  xn+1 from Central Bright.  Then according to Youngs experiment,

xn = (nλD)/d----------(1)

xn+1 =((n+1)λD)/d) ---------------(2)

xn+1 - xn   =((n+1) λD)/d) – (nλD)/d)

xn+1 - xn   =(n+1-n)  λD)/d

xn+1 - xn = (λD)/d

Fringe width of Dark Bands: Let us consider two adjacent Dark frindge at a distance xm  and  xm+1 from Central Bright.  Then according to Youngs experiment,

xm = ((2m-1) λD)/2d----------(1)

xm+1 =(2(m+1-1) λD)/2d)-----------(2)

xm+1 -  xm = (2(m+1)-1-2m+1) λD/2d)

xm+1 - xm = (λD)/d

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