In a double-slit experiment, the two slits have a finite width a and are separated by a distance d . The interference pattern is observed on a distant screen. It is found that exactly 11 bright interference fringes (including the central fringe) are observed within the central maximum of the diffraction envelope, with the adjacent bright fringes being missing orders. The ratio of the slit separation to the slit width

Step-by-step solution

In a double-slit experiment with slits of finite width, the interference pattern is modulated by the single-slit diffraction envelope. The angular position of the first minimum of the diffraction envelope is given by: = a The angular position of the m -th order interference maximum is: _m = m d For exactly 11 bright interference fringes to be visible inside the central diffraction maximum, there must be 5 fringes on either side of the central maximum ( 5 + 5 + 1 = 11 ). Since the adjacent bright fringes are missing