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^{4}m. 

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 


