Derive the mathematical expression for the spacing of bright (or dark) fringes in Young’s double-slit experiment.
(a) Starting from the geometry of two parallel slits separated by a distance d and a screen kept at a distance D(D≫d), obtain the condition for constructive interference at a point on the screen in terms of the path difference.
(b) Using the condition obtained in part (a), derive an expression for the distance yn of the n-th bright fringe from the central maxima.
(c) Hence, show that the fringe width β is given by β=dλD, where the symbols have their usual meanings.