Wave Optics: Interference & Diffraction
Huygens' principle, double-slit interference, and single-slit diffraction patterns.
Light is a wave; superposition of two coherent sources produces interference. For Young's two-slit experiment with slit separation $d$ and wavelength $\lambda$, constructive maxima occur at angles satisfying
$$d \sin\theta = m\lambda, \qquad m = 0, \pm 1, \pm 2, \ldots$$A single slit of width $a$ produces a diffraction envelope with minima at $a \sin\theta = m\lambda$ ($m \neq 0$). The full two-slit pattern is the product: a rapid interference fringe pattern modulated by the slow diffraction envelope.
A diffraction grating with $N$ slits sharpens the bright orders; the resolving power scales with $N$ — the principle behind spectrometers.