A student wishes to record a diffraction pattern on a 6.0cm-wide photographic plate that is positioned 1.8m from a single slit. The plate is centered on the direct line of the incident beam, so it extends 3.0cm to either side of the beam axis. The incident light has a wavelength of 450nm. The student wants the plate to show no more than five dark fringes in total (that is, at most five minima across the entire width of the plate).
(a) Derive an inequality that the slit width a must satisfy in order to meet the student’s requirement.
(b) Using the inequality from part (a), determine the largest allowable numerical value of the slit width.