Light Bends and Spreads at an Edge
When light passes a narrow slit or a sharp edge it does not go straight; it bends and spreads. The single-slit pattern is a sinc² curve, but here that is a classical intensity of light, not the quantum probability density of the qm track. The diffraction grating of many slits and the Huygens wavelet picture are entirely new compared with the quantum track.
When light passes a single slit of width a, the screen shows a bright central peak flanked by dark minima. The minima appear where a·sinθ = mλ, and the intensity follows a sinc² shape. The narrower the slit, the wider the diffraction spreads. Because the first minimum sits at sinθ = λ/a, the spread is set by the ratio of wavelength to slit width, and once the slit narrows to about one wavelength the light fans out into nearly a half circle.
Huygens said every point on a wavefront acts as a source of a new wavelet. Adding the wavelets from many sources across the slit, direction by direction, they reinforce and cancel to build the diffraction pattern. The more sources you pack in, the closer their sum settles onto the smooth sinc² envelope. Straight ahead every wavelet arrives in phase and adds up fully, while toward the sides the phases slip apart and cancel, which is why the center is brightest.
A diffraction grating is many slits placed at regular spacing. As the number of slits N grows, the principal maxima stay at the same places but become steadily sharper and brighter. Their positions are set by d·sinθ = mλ, where d is the spacing between neighboring slits. The more slits there are, the more completely the light between peaks cancels, so the peak width narrows in proportion to 1/N, which is why a spectrometer rules thousands of lines to separate wavelengths ever more finely.
On the same grating, a different wavelength λ diffracts to a different angle. Since d·sinθ = mλ, a longer λ means a larger angle, so many colors fan out. Splitting light by wavelength this way is the heart of spectroscopy. When mλ exceeds d, that order cannot appear. The rainbow sheen on a CD or DVD comes from the same effect, its fine grooves acting as a grating that splits white light by wavelength.
Now drag a probe across the pattern yourself. Read the angle θ at each spot, and use the integer m in a·sinθ = mλ to see which minimum you are on. At the center the intensity is largest, and a dark minimum sits at each integer m in a regular row. Between the dark minima sit progressively fainter side peaks, the side lobes of the sinc² curve, each far weaker than the central one.