Chapter 35, Problem 48P

(II) Missing orders occur for a diffraction grating when a diffraction minimum coincides with an interference maximum. Let D be the width of each slit and d the separation of slits. (a) Show that if d = 2D, all even orders (m = 2, 4, 6, ⋯) are missing. (b) Show there will be missing orders whenever

$\frac{d}{D}=\frac{m_1}{m_2}$

where m₁ and m₂ are integers. (c) Discusss the case d = D, the limit in which the space between slits becomes negligible.