Past exam of the physics A course of the University of Cambridge / 2011 / Paper 1 / Section B / B8 / a (slit width) / Solution

With $w=1.0\mu \mathrm{m}$ the order positions are unchanged from the grating equation, and the envelope's first zeros satisfy $|\sin \theta |=\lambda /w$. Equivalently the first missing integer orders are $m=\pm 5$. The third-order peaks remain appreciable. The displayed order-coordinate $s=p\sin \theta /\lambda$ places all principal maxima at integers.