In a Young's double-slit experiment, the finite width of the slits creates a diffraction envelope that modulates the interference pattern. If the distance between the slits is exactly 3 times the width of each individual slit, the total number of primary interference maxima that lie strictly within the central diffraction maximum is:

Step-by-step solution

Let the width of each slit be a and the distance between the slits be d . We are given that d = 3a . The central diffraction maximum is bounded by the first diffraction minima, which occur at angles given by: a = = a The interference maxima occur at angles given by: d = n where n is an integer ( n = 0, 1, 2, ). Substituting d = 3a into the interference condition: 3a = n = n 3a For the interference maxima to lie strictly within the central diffraction maximum, the angle must satisfy: - a Substituting the expression