Discussion on First Minimum

Considering the first-minimum condition $\sin\theta=\lambda/a$ in special cases: (i) if $a<\lambda$, diffraction cannot occur at all, since $\sin\theta$ can never exceed 1; (ii) if $a\geq\lambda$, diffraction is possible -- for $a=\lambda$ exactly, $\sin\theta=1$, i.e. $\theta=90°$, so the central maximum spreads fully into the geometrically shadowed region, bending the light through a full $90°$; for $a\gg\lambda$, $\sin\theta\ll1$, meaning the predicted first minimum falls essentially within the width of the slit itself, so diffraction is not noticed at all and straight-line (ray-optics) propagation is effectively recovered; (iii) for $a$ comparable to but greater than $\lambda$, say $a=2\lambda$, diffraction is noticeable at a practical, measurable angle (e.g. $\ …