Diffraction

Diffraction is most pronounced when the size of the opening is comparable to the wavelength, so narrowing a slit spreads the wave further and widening it makes the transmitted beam more nearly straight. What decides the behaviour is the ratio $\lambda/a$, which is why a doorway floods the next room with sound and casts a sharp shadow in light. For a single slit of width $a$, the relation $a\sin\theta = m\lambda$ with $m = 1, 2, 3$ locates the dark fringes, and the bright central maximum sits between the first two minima and is twice as wide as the fringes beyond it.

Three errors dominate. Predicting that a wider opening spreads a wave further, when the angle in $\sin\theta = \lambda/a$ grows as the opening narrows. Deciding whether a wave diffracts by asking whether the opening looks small in everyday terms rather than comparing it with the wavelength. And treating $a\sin\theta = m\lambda$ as the condition for bright fringes, carried over from the double slit, which puts bright bands exactly where the screen is dark.