Diffraction

The CED puts the size condition plainly: diffraction is most pronounced when the size of the opening is comparable to the wavelength of the wave. A doorway is metres across and audible sound has a wavelength of about a metre, so you hear round corners; visible light has a wavelength near $5 \times 10^{-7}$ m, so it does not visibly bend round the same doorway. Narrow the slit and the pattern opens out, which is the reverse of what intuition suggests.

For a single slit of width $a$, the sheet's condition locates the dark fringes.

with $m = 1, 2, 3, \ldots$ and no $m = 0$. That is the reverse of the double slit, where the same shape of equation gives the bright fringes, and it is the trap on this topic. The subscript on $y_{\text{min}}$ is the sheet telling you which fringe you are locating.

The small-angle form is only valid below about 10 degrees; the AP Physics 2 conventions block says the approximation applies to single- and double-slit diffraction.

Two consequences worth carrying. The central bright band is twice as wide as the others, of width $2\lambda L / a$, which is not printed and has to be derived. And a diffraction grating or double slit still has its pattern shaped by the single-slit envelope of each individual opening. Topic 14.7 has the CED statements.