A single slit of width a and a double slit with separation d = 3a are illuminated by the same monochromatic light. The total angular divergence between the second order minima in the single slit diffraction pattern is equal to the angular position of the N -th order bright fringe from the central maximum in the double slit interference pattern. The value of N is ______.

Step-by-step solution

For a single slit of width a , the angular position of the n -th order minimum is = n a . The total angular divergence between the second order minima ( n=2 ) is 2 = 2(2 ) a = 4 a . For a double slit with separation d , the angular position of the N -th order bright fringe is ' = N d . Given d = 3a , we have ' = N 3a . Equating the two angles as given: 4 a = N 3a 4 = N 3 N = 12 . Answer: 12