In a Young's double slit experiment employing white light, determine the minimum order of the violet fringe ( = 400 nm ) that overlaps with a red fringe ( = 700 nm ).

Step-by-step solution

Let n_v be the order of the violet fringe and n_r be the order of the red fringe. The position of the n -th bright fringe in Young's double slit experiment is given by y = n D d . For the fringes to overlap, their positions on the screen must be the same: n_v _v D d = n_r _r D d n_v _v = n_r _r Substituting the given wavelengths _v = 400 nm and _r = 700 nm : n_v (400) = n_r (700) 4 n_v = 7 n_r To find the minimum order, n_v and n_r must be the smallest possible positive integers. Since 4 and 7 are coprime, we get: