Derivation of Young's Slits Equation


For the central bright fringe, the path difference is 0. 


S2O - S1O = 0.


For the first bright fringe

 S2Q - S1Q = l


Notice that in the triangle S1S2Z, S2Z is l. 


We know that S1S2 is s. 



sin q = l/s.


For the triangle OPQ, tan f = w/D.  Although in this diagram, it is clear that q f, in the real thing, we can assume that q = f, as the real set up is very much longer.


We know that for small angles sin q = tan q.







To produce easily measurable fringes, D must be large i.e. in metres while s is small (<1 mm). The larger D is the less bright the fringes.  We can increase the width of the fringes by increasing the wavelength, or by decreasing the slit width.


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