Consider a periodic array of slits with a period of \Lambda through which light propagates. Let \theta be the angle of incidence. Show that diffraction occurs at angles \theta' that satisfy the following equation:
\Lambda \sin\theta + \Lambda \sin\theta' = m\Lambda, m = 1,2,3,...
(b) Let z be the direction of periodicity. Show that the equation above can also be written as
k'_z - k_z = m(2\pi/\Lambda), m = 1,2,3,...