The fringe width (β) is defined as the distance between two consecutive bright fringes:$\beta = y_{n+1} - y_n = \frac{(n+1)\lambda D}{d} - \frac{n\lambda D}{d} = \frac{\lambda D}{d}$Similarly, the distance between two consecutive dark fringes:$\beta = y'_{n+1} - y'_n = \frac{(2n+1)\lambda D}{2d} - \frac{(2n-1)\lambda D}{2d} = \frac{\lambda D}{d}$Since both expressions give the same value, the fringe widths for bright and dark fringes are equal.