14.5 Multiple Slits and Diffraction Gratings (AHL)

As slit count increases, principal maxima become narrower and more intense while side lobes weaken. Physically, more coherent emitters impose a stricter phase-matching requirement for strong constructive interference, so bright peaks occupy smaller angular ranges.

This is why gratings are powerful for wavelength analysis. A two-slit pattern is useful for demonstrating wave nature, but a many-slit grating creates sharp angular peaks that separate nearby wavelengths more clearly.

If line density is L lines per meter, then d = 1/L. Larger line density means smaller d and typically larger diffraction angles for a given order. This increases angular dispersion, which helps spectral separation but can also cause order overlap when bandwidth is broad.

Increasing order n improves resolution, but usable order is capped by the condition |n lambda / d| <= 1. In white-light applications, different wavelength-order combinations can land at similar angles, producing overlap. Practical instrument design balances dispersion, intensity, and overlap risk.