A conducting wall blocks a plane wave except for one narrow opening. If light were rays, you'd get a sharp beam the width of the slit. Instead, the wave spreads.
This is diffraction. The wave arriving at the slit opening has no information about the wall, so each point in the opening propagates forward as if it were a new source. The narrower the slit relative to the wavelength, the more the wave fans out.
Narrow the slit down to a few cells and the transmitted wave becomes nearly semicircular. Widen it and the beam tightens up.
Two slits, two spreading waves. They overlap, and the fields add point by point, the same superposition from Chapter I.
Where the path difference from the two slits is a whole number of wavelengths, peaks align. Where it's off by half a wavelength, they cancel. The result: alternating bright and dark fringes.
Young ran this experiment in 1801 and saw the same fringes, projected on a wall. Just like Snell's law, we never coded interference: the pattern emerges from the field equations on its own.
Wider slit separation leads to tighter fringes.
Add more slits and the bright fringes sharpen. With two slits, the peaks are broad. With many, they collapse into narrow, intense beams.
Constructive interference now requires all slits to be in phase, which only happens at very specific angles. Everywhere else, the contributions from different slits cancel each other out.
Real diffraction gratings have thousands of slits per millimeter. The beams are sharp enough to separate individual wavelengths, which is how spectrometers work.
The diffraction angle depends on the ratio of wavelength to slit spacing:
d sin θ = m λ
d is the slit spacing and λ is the wavelength. Each integer m (0, 1, 2, ...) is a direction where the path difference between adjacent slits is exactly m whole wavelengths. Longer wavelengths diffract at a wider angle.
Lower frequency results in a longer wavelength, which causes the beams to swing outward. Changing the incidence angle shifts the entire diffraction pattern. This is why a grating splits white light into a spectrum: each frequency diffracts at its own angle.