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Young's Experiment: Calculation of the Fringe Spacing
We will see here how to calculate the distance between one bright fringe and the next, the fringe spacing, in Young's double slit experiment.  
   
The diagram below shows rays of light from the two slits a and b.  
These rays are at angle θ to the normal line.  
We assume that these rays meet at a point on a screen about 2m away and that the first bright fringe is observed at this point.  
However, remember that the distance, d between the two slits is of the order of 10-4m.  
This means that we can reasonably approximate these rays to be parallel.  
   
 
This being the first bright fringe, the path difference must be equal to one wavelength, λ.
   
The next diagram is an even more enlarged view of the slits.  
 
From this view it is clear that the path difference is given by  
 
So, for the first bright fringe, we have  
 
and other bright fringes will occur at path differences of 2λ, 3λ etc  
Therefore, for a bright fringe, we have  
 
where n = 0, 1, 2, 3 etc  
   
For the next view, we zoom out to see the whole apparatus (not to scale)
   
   
θ is the angular separation of the bright fringes.  
s is their linear separation or fringe spacing  
θ is a very small angle (much smaller than on this diagram) so will can use the approximation that sinθ = θ in radians.  
For the first bright fringe, n = 1   
This means that the equation above becomes  
   
Therefore, the fringe spacing, s is given by  
 
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